Edit Profile Götze, Friedrich W. Compute Distance To: Compute Author ID: gotze.friedrich-w Published as: Goetze, F.; Götze, F.; Götze, Friedrich Homepage: https://www.math.uni-bielefeld.de/~goetze/ External Links: MGP · Math-Net.Ru · Wikidata · ORCID · ResearchGate · dblp · GND Documents Indexed: 216 Publications since 1978, including 4 Books Reviewing Activity: 36 Reviews Biographic References: 1 Publication all top 5 Co-Authors 17 single-authored 34 Tikhomirov, Alexander Nikolaevich 31 Bobkov, Sergey Germanovich 30 Chistyakov, Gennadiy P. 21 Bernik, Vasiliĭ Ivanovich 20 Bentkus, Vidmants-Kastytis 16 Zaitsev, Andrei Yu. 14 Naumov, Alekseĭ Aleksandrovich 10 van Zwet, Willem Rutger 9 Bloznelis, Mindaugas 8 Gusakova, Anna Grigorevna 8 Ul’yanov, Vladimir Vasil’evich 8 Zaporozhets, Dmitry 7 Beresnevich, Victor V. 7 Kukso, Olga 6 Hipp, Christian 6 Prokhorov, Yuriĭ Vasil’evich 5 Bickel, Peter John 5 Kaliada, Dzianis 5 Paulauskas, Vygantas Ionovič 4 Budarina, Natalia Viktorovna 4 Račkauskas, Alfredas Yurgevich 4 Sambale, Holger 3 Alexeev, Nikita V. 3 Eliseeva, Yulia S. 3 Gordin, Mikhail Iosifovich 3 Kösters, Holger 3 Timushev, Dmitry Anatolievich 3 Zitikis, Ričardas 2 Baake, Michael 2 Bhattacharya, Rabi N. 2 Giné-Masdéu, Evarist 1 Baumeister, Barbara 1 Bogatyrev, Sergey Anatolievich 1 Bolthausen, Erwin 1 Bux, Kai-Uwe 1 Dzindzalieta, Dainius 1 Erdős, László 1 Guionnet, Alice 1 Heinrich, Lothar 1 Hoffmann, Werner 1 Houdré, Christian 1 Huck, Christian 1 Jakobi, Tobias 1 Jaworski, Jerzy 1 Kabluchko, Zakhar A. 1 Kalosha, Nikolai I. 1 Kielak, Dawid 1 Kirsch, Werner 1 Klopp, Frédéric 1 Krause, Henning 1 Kriecherbauer, Thomas 1 Künsch, Hans Rudolf 1 Lehner, Franz 1 Levina, Alla B. 1 Mason, David M. 1 Merkl, Franz 1 Milbrodt, Hartmut 1 Sinulis, Arthur 1 Spokoiny, Vladimir G. 1 Venker, Martin 1 Yurchenko, Vladimir B. 1 Zalesskij, Boris Andreevich all top 5 Serials 20 The Annals of Probability 17 Theory of Probability and its Applications 12 Probability Theory and Related Fields 12 Journal of Mathematical Sciences (New York) 12 Bernoulli 9 Journal of Theoretical Probability 7 Lithuanian Mathematical Journal 6 The Annals of Statistics 6 Doklady Mathematics 5 Doklady Natsional’noĭ Akademii Nauk Belarusi 4 Teoriya Veroyatnosteĭ i eë Primeneniya 4 Journal of Multivariate Analysis 4 Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 4 Zapiski Nauchnykh Seminarov POMI 4 Mathematical Methods of Statistics 4 Central European Journal of Mathematics 3 Acta Arithmetica 3 Random Matrices: Theory and Applications 2 Communications in Mathematical Physics 2 Scandinavian Journal of Statistics 2 Advances in Mathematics 2 Journal of Applied Probability 2 Journal of Functional Analysis 2 Acta Applicandae Mathematicae 2 Stochastic Processes and their Applications 2 Electronic Journal of Probability 2 Electronic Communications in Probability 2 Izvestiya: Mathematics 2 Documenta Mathematica 2 Communications in Contemporary Mathematics 2 Oberwolfach Reports 2 Chebyshevskiĭ Sbornik 2 Dal’nevostochnyĭ Matematicheskiĭ Zhurnal 1 IEEE Transactions on Information Theory 1 Journal of Statistical Physics 1 Mathematical Notes 1 Mitteilungen der Deutschen Mathematiker-Vereinigung (DMV) 1 Russian Mathematical Surveys 1 Compositio Mathematica 1 Inventiones Mathematicae 1 Journal of Number Theory 1 Proceedings of the American Mathematical Society 1 Siberian Mathematical Journal 1 Probability and Mathematical Statistics 1 Forum Mathematicum 1 St. Petersburg Mathematical Journal 1 Statistica Sinica 1 Annals of Mathematics. Second Series 1 Acta Physica Polonica B 1 Acta Crystallographica. Section A 1 Moscow Journal of Combinatorics and Number Theory 1 European Journal of Mathematics 1 Zhurnal Belorusskogo Gosudarstvennogo Universiteta. Matematika. Informatika 1 EMS Series of Congress Reports all top 5 Fields 153 Probability theory and stochastic processes (60-XX) 58 Statistics (62-XX) 44 Number theory (11-XX) 20 Linear and multilinear algebra; matrix theory (15-XX) 8 Functional analysis (46-XX) 7 Real functions (26-XX) 6 History and biography (01-XX) 6 Statistical mechanics, structure of matter (82-XX) 4 General and overarching topics; collections (00-XX) 4 Combinatorics (05-XX) 4 Information and communication theory, circuits (94-XX) 3 Approximations and expansions (41-XX) 3 Convex and discrete geometry (52-XX) 3 Computer science (68-XX) 2 Order, lattices, ordered algebraic structures (06-XX) 2 Topological groups, Lie groups (22-XX) 1 Group theory and generalizations (20-XX) 1 Measure and integration (28-XX) 1 Functions of a complex variable (30-XX) 1 Special functions (33-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Differential geometry (53-XX) 1 Manifolds and cell complexes (57-XX) 1 Quantum theory (81-XX) 1 Operations research, mathematical programming (90-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH 163 Publications have been cited 1,742 times in 1,157 Documents Cited by ▼ Year ▼ Exponential integrability and transportation cost related to logarithmic Sobolev inequalities. Zbl 0924.46027Bobkov, S. G.; Götze, F. 193 1999 When is the Student \(t\)-statistic asymptotically standard normal? Zbl 0958.60023Giné, Evarist; Götze, Friedrich; Mason, David M. 96 1997 Resampling fewer than \(n\) observations: gains, losses, and remedies for losses. Zbl 0927.62043Bickel, P. J.; Götze, F.; van Zwet, W. R. 91 1997 On the rate of convergence in the multivariate CLT. Zbl 0729.62051Götze, F. 56 1991 Asymptotic expansions for sums of weakly dependent random vectors. Zbl 0497.60022Goetze, F.; Hipp, C. 56 1983 The circular law for random matrices. Zbl 1203.60010Götze, Friedrich; Tikhomirov, Alexander 55 2010 Second-order correctness of the blockwise bootstrap for stationary observations. Zbl 0906.62040Götze, F.; Künsch, H. R. 49 1996 The Edgeworth expansion for U-statistics of degree two. Zbl 0614.62015Bickel, P. J.; Götze, F.; van Zwet, W. R. 49 1986 The Berry-Esseen bound for Student’s statistic. Zbl 0855.62009Bentkus, V.; Götze, F. 44 1996 Asymptotic expansions for bivariate von Mises functionals. Zbl 0405.60009Götze, F. 40 1979 Rate of convergence to the semi-circular law. Zbl 1031.60019Götze, F.; Tikhomirov, A. 28 2003 Asymptotic expansions in the central limit theorem under moment conditions. Zbl 0369.60027Götze, F.; Hipp, C. 27 1978 An Edgeworth expansion for symmetric statistics. Zbl 0920.62016Bentkus, V.; Götze, F.; van Zwet, W. R. 26 1997 Lattice point problems and values of quadratic forms. Zbl 1090.11063Götze, Friedrich 22 2004 The arithmetic of distributions in free probability theory. Zbl 1239.46046Chistyakov, Gennadii P.; Götze, Friedrich 20 2011 Asymptotic distribution of singular values of powers of random matrices. Zbl 1208.60021Alexeev, N.; Götze, F.; Tikhomirov, A. 20 2010 The distribution of close conjugate algebraic numbers. Zbl 1206.11091Beresnevich, Victor; Bernik, Vasili; Götze, Friedrich 20 2010 Asymptotic distribution of statistics in time series. Zbl 0827.62015Götze, F.; Hipp, C. 20 1994 Limit distributions of Studentized means. Zbl 1056.60020Chistyakov, G. P.; Götze, F. 19 2004 Lattice point problems and distribution of values of quadratic forms. Zbl 0979.11048Bentkus, V.; Götze, F. 19 1999 Discrete isoperimetric and Poincaré-type inequalities. Zbl 0940.60028Bobkov, S. G.; Götze, F. 18 1999 Limit theorems in free probability theory. I. Zbl 1157.46037Chistyakov, G. P.; Götze, F. 17 2008 The rate of convergence for spectra of GUE and LUE matrix ensembles. Zbl 1108.60014Götze, Friedrich; Tikhomirov, Alexander 17 2005 Rate of convergence in probability to the Marchenko-Pastur law. Zbl 1049.60018Götze, Friedrich; Tikhomirov, Alexander 17 2004 A Berry-Esséen bound for Student’s statistic in the non-i. i. d. case. Zbl 0923.60029Bentkus, V.; Bloznelis, M.; Götze, F. 17 1996 Optimal rates of convergence in the CLT for quadratic forms. Zbl 0858.62010Bentkus, V.; Götze, F. 17 1996 Orthogonal decomposition of finite population statistics and its applications to distributional asymptotics. Zbl 1012.62009Bloznelis, M.; Götze, F. 16 2001 Asymptotic distribution of quadratic forms. Zbl 0941.60049Götze, F.; Tikhomirov, A. N. 16 1999 On Edgeworth expansions in Banach spaces. Zbl 0473.60009Goetze, F. 16 1981 Berry-Esseen bounds in the entropic central limit theorem. Zbl 1307.60011Bobkov, Sergey G.; Chistyakov, Gennadiy P.; Götze, Friedrich 15 2014 Concentration inequalities and limit theorems for randomized sums. Zbl 1111.60014Bobkov, Sergey G.; Götze, Friedrich 15 2007 Fisher information and the central limit theorem. Zbl 1372.60018Bobkov, Sergey G.; Chistyakov, Gennadiy P.; Götze, Friedrich 14 2014 The rate of convergence for multivariate sampling statistics. Zbl 0798.62023Bolthausen, Erwin; Götze, Friedrich 14 1993 Rate of convergence and Edgeworth-type expansion in the entropic central limit theorem. Zbl 1296.60051Bobkov, Sergey G.; Chistyakov, Gennadiy P.; Götze, Friedrich 13 2013 Lower bounds for the number of integral polynomials with given order of discriminants. Zbl 1222.11096Bernik, Vasili; Götze, Friedrich; Kukso, Olga 13 2008 On Gaussian and Bernoulli covariance representations. Zbl 1053.60019Bobkov, Sergey G.; Götze, Friedrich; Houdré, Christian 13 2001 On the singular spectrum of powers and products of random matrices. Zbl 1211.60003Alexeev, N. V.; Götze, F.; Tikhomirov, A. N. 12 2010 On concentration of empirical measures and convergence to the semi-circle law. Zbl 1247.60010Bobkov, S. G.; Götze, F.; Tikhomirov, A. N. 11 2010 On the second-order correlation function of the characteristic polynomial of a Hermitian Wigner matrix. Zbl 1193.15035Götze, F.; Kösters, H. 11 2009 Uniform rates of convergence in the CLT for quadratic forms in multidimensional spaces. Zbl 0888.60021Bentkus, V.; Götze, F. 10 1997 On the lattice point problem for ellipsoid. Zbl 0871.11069Bentkus, V.; Götze, F. 10 1997 On the local semicircular law for Wigner ensembles. Zbl 1429.60010Götze, Friedrich; Naumov, Alexey; Tikhomirov, Alexander; Timushev, Dmitry 9 2018 Integral polynomials with small discriminants and resultants. Zbl 1339.11073Beresnevich, Victor; Bernik, Vasili; Götze, Friedrich 9 2016 Asymptotic distribution of quadratic forms and applications. Zbl 1002.60018Götze, F.; Tikhomirov, A. 9 2002 The accuracy of Gaussian approximation in Banach spaces. Zbl 0960.60008Bentkus, V.; Götze, F.; Paulauskas, V.; Račkauskas, A. 9 2000 Optimal bounds in non-Gaussian limit theorems for \(U\)-statistics. Zbl 1008.62017Bentkus, V.; Götze, F. 9 1999 Lower estimates of the convergence rate for \(U\)-statistics. Zbl 0839.60023Bentkus, Vidmantas; Götze, Friedrich; Zitikis, Ričardas 9 1994 Approximations for multivariate U-statistics. Zbl 0624.62028Götze, F. 9 1987 Distribution of complex algebraic numbers. Zbl 1350.11087Götze, Friedrich; Kaliada, Dzianis; Zaporozhets, Dmitry 8 2017 Local universality of repulsive particle systems and random matrices. Zbl 1301.60009Götze, Friedrich; Venker, Martin 8 2014 Limit theorems for spectra of random matrices with martingale structure. Zbl 1118.15022Götze, F.; Tikhomirov, A. N. 8 2007 Adaptive choice of bootstrap sample sizes. Zbl 1373.62177Götze, Friedrich; Račkauskas, Alfredas 8 2001 Accuracy of Gaussian approximation in Banach spaces. Zbl 0797.60010Bentkus, V.; Götze, F.; Paulauskas, V.; Račkauskas, A. 8 1991 Edgeworth expansions in functional limit theorems. Zbl 0689.60038Götze, F. 8 1989 On the rate of convergence in the central limit theorem in Banach spaces. Zbl 0599.60009Götze, F. 8 1986 Local semicircle law under moment conditions: the Stieltjes transform, rigidity, and delocalization. Zbl 1426.15056Götze, F.; Naumov, A. A.; Tikhomirov, A. N. 7 2018 Optimal bounds for convergence of expected spectral distributions to the semi-circular law. Zbl 1338.60014Götze, F.; Tikhomirov, A. 7 2016 Estimates for the concentration functions in the Littlewood-Offord problem. Zbl 1332.15093Eliseeva, Yu. S.; Götze, F.; Zaitsev, A. Yu. 7 2015 Asymptotic spectra of matrix-valued functions of independent random matrices and free probability. Zbl 1331.60019Götze, F.; Kösters, H.; Tikhomirov, A. 7 2015 Distribution of real algebraic numbers of arbitrary degree in short intervals. Zbl 1334.11058Bernik, V. I.; Götze, F. 7 2015 The asymptotic number of integral cubic polynomials with bounded heights and discriminants. Zbl 1322.11078Kaliada, Dzianis; Götze, Friedrich; Kukso, Olga 7 2014 On the divisibility of the discriminant of an integral polynomial by prime powers. Zbl 1228.11111Bernik, V.; Götze, F.; Kukso, O. 7 2008 An Edgeworth expansion for finite-population \(U\)-statistics. Zbl 0982.62009Bloznelis, Mindaugas; Götze, Friedrich 7 2000 Estimates for the rapid decay of concentration functions of \(n\)-fold convolutions. Zbl 0936.60014Götze, F.; Zaitsev, A. Yu. 7 1998 Asymptotic expansions in the CLT in free probability. Zbl 1282.46059Chistyakov, G. P.; Götze, F. 6 2013 Entropic instability of Cramer’s characterization of the normal law. Zbl 1371.60005Bobkov, S. G.; Chistyakov, G. P.; Götze, F. 6 2012 Non-uniform bounds in local limit theorems in case of fractional moments. I. Zbl 1239.60016Bobkov, S. G.; Chistyakov, G. P.; Götze, F. 6 2011 Simultaneous approximations of zero by an integral polynomial its derivative, and small values of discriminants. Zbl 1267.11079Beresnevich, V. V.; Bernik, V. I.; Götze, F. 6 2010 Bounds for the rate of strong approximation in the multidimensional invariance principle. Zbl 1196.60053Götze, F.; Zaitsev, A. Yu. 6 2009 An Edgeworth expansion for symmetric finite population statistics. Zbl 1010.62017Bloznelis, M.; Götze, F. 6 2002 On the lattice point problem for ellipsoids. Zbl 0879.11053Bentkus, V.; Götze, F. 6 1995 A simple analysis of third-order efficiency of estimates. Zbl 1373.62093Bickel, Peter J.; Götze, Friedrich; van Zwet, W. R. 6 1985 Higher order concentration for functions of weakly dependent random variables. Zbl 07107392Götze, Friedrich; Sambale, Holger; Sinulis, Arthur 5 2019 On points with algebraically conjugate coordinates close to smooth curves. Zbl 1375.11058Bernik, Vasilii; Götze, Friedrich; Gusakova, A. 5 2016 On minimal singular values of random matrices with correlated entries. Zbl 1348.15023Götze, F.; Naumov, A.; Tikhomirov, A. 5 2015 Fisher information and convergence to stable laws. Zbl 1315.60031Bobkov, S. G.; Chistyakov, G. P.; Götze, F. 5 2014 Explicit rates of approximation in the CLT for quadratic forms. Zbl 1290.60021Götze, Friedrich; Zaitsev, Andrei Yu. 5 2014 Distance between conjugate algebraic numbers in clusters. Zbl 1284.11051Budarina, N. V.; Goetze, F. 5 2013 Distribution of algebraic numbers and metric theory of Diophantine approximation. Zbl 1316.11063Bernik, V.; Beresnevich, V.; Götze, F.; Kukso, O. 5 2013 Bounds for characteristic functions in terms of quantiles and entropy. Zbl 1258.60022Bobkov, Sergey G.; Chistyakov, Gennadiy P.; Götze, Friedrich 5 2012 Limit correlation functions for fixed trace random matrix ensembles. Zbl 1165.82016Götze, Friedrich; Gordin, Mikhail 5 2008 Limit theorems in free probability theory II. Zbl 1148.46035Chistyakov, Gennadii P.; Götze, Friedrich 5 2008 Limit theorems for spectra of positive random matrices under dependence. Zbl 1075.60017Götze, F.; Tikhomirov, A. 5 2004 Bounds for the accuracy of Poissonian approximations of stable laws. Zbl 0885.62014Bentkus, V.; Götze, F.; Paulauskas, V. 5 1996 Asymptotic expansions for potential functions of I.I.D. random fields. Zbl 0659.60035Götze, F.; Hipp, C. 5 1989 Asymptotic expansions in functional limit theorems. Zbl 0557.60027Götze, F. 5 1985 Correlation functions of real zeros of random polynomials. Zbl 1386.60188Götze, F.; Kaliada, D.; Zaporozhets, D. 4 2018 Local laws for non-Hermitian random matrices. Zbl 1392.60012Götze, F.; Naumov, A. A.; Tikhomirov, A. N. 4 2017 Second-order concentration on the sphere. Zbl 1373.60043Bobkov, Sergey G.; Chistyakov, Gennadiy P.; Götze, Friedrich 4 2017 Arak’s inequalities for concentration functions and the Littlewood-Offord problem. Zbl 1360.60041Götze, F.; Eliseeva, Yu. S.; Zaitsev, A. Yu. 4 2016 Limit theorems for two classes of random matrices with dependent entries. Zbl 1314.60026Götze, F.; Naumov, A. A.; Tikhomirov, A. N. 4 2015 Resampling fewer than \(n\) observations: gains, losses, and remedies for losses. Zbl 1373.62173Bickel, P. J.; Götze, F.; van Zwet, W. R. 4 2012 Concentration of empirical distribution functions with applications to non-i.i.d. models. Zbl 1207.62106Bobkov, S. G.; Götze, F. 4 2010 The rate of convergence of spectra of sample covariance matrices. Zbl 1210.60013Götze, F.; Tikhomirov, A. N. 4 2009 Limit correlation functions at zero for fixed trace random matrix ensembles. Zbl 1153.60026Götze, F.; Gordin, M. I.; Levina, A. 4 2007 Asymptotic expansions in non-central limit theorems for quadratic forms. Zbl 1089.60017Götze, F.; Tikhomirov, A. N. 4 2005 Rate of convergence to the semicircular law for the Gaussian unitary ensemble. Zbl 1041.60033Götze, F.; Tikhomirov, A. N. 4 2002 A multiplicative inequality for concentration functions of \(n\)-fold convolutions. Zbl 0969.60023Götze, Friedrich; Zaitsev, Andrei Yu. 4 2000 Lattice point problems and the central limit theorem in Euclidean spaces. Zbl 0906.60023Götze, F. 4 1998 Approximation of quadratic forms of independent random vectors by accompanying laws. Zbl 0913.60034Bentkus, V.; Götze, F.; Zaitsev, A. Yu. 4 1997 Joint distribution of conjugate algebraic numbers: a random polynomial approach. Zbl 1443.11199Götze, Friedrich; Koleda, Denis; Zaporozhets, Dmitry 2 2020 Higher order concentration for functions of weakly dependent random variables. Zbl 07107392Götze, Friedrich; Sambale, Holger; Sinulis, Arthur 5 2019 Rényi divergence and the central limit theorem. Zbl 07036338Bobkov, S. G.; Chistyakov, G. P.; Götze, F. 3 2019 Non-uniform bounds in the Poisson approximation with applications to informational distances. I. Zbl 1432.62034Bobkov, S. G.; Chistyakov, G. P.; Götze, F. 1 2019 Gaussian mixtures and normal approximation for V. N. Sudakov’s typical distributions. Zbl 07084418Bobkov, S. G.; Chistyakov, G. P.; Götze, F. 1 2019 Higher order concentration of measure. Zbl 1447.60049Bobkov, Sergey G.; Götze, Friedrich; Sambale, Holger 1 2019 On the local semicircular law for Wigner ensembles. Zbl 1429.60010Götze, Friedrich; Naumov, Alexey; Tikhomirov, Alexander; Timushev, Dmitry 9 2018 Local semicircle law under moment conditions: the Stieltjes transform, rigidity, and delocalization. Zbl 1426.15056Götze, F.; Naumov, A. A.; Tikhomirov, A. N. 7 2018 Correlation functions of real zeros of random polynomials. Zbl 1386.60188Götze, F.; Kaliada, D.; Zaporozhets, D. 4 2018 New applications of Arak’s inequalities to the Littlewood-Offord problem. Zbl 1392.60041Götze, Friedrich; Zaitsev, Andrei Yu. 3 2018 Berry-Esseen bounds for typical weighted sums. Zbl 1414.60012Bobkov, S. G.; Chistyakov, G. P.; Götze, F. 2 2018 Distribution of complex algebraic numbers. Zbl 1350.11087Götze, Friedrich; Kaliada, Dzianis; Zaporozhets, Dmitry 8 2017 Local laws for non-Hermitian random matrices. Zbl 1392.60012Götze, F.; Naumov, A. A.; Tikhomirov, A. N. 4 2017 Second-order concentration on the sphere. Zbl 1373.60043Bobkov, Sergey G.; Chistyakov, Gennadiy P.; Götze, Friedrich 4 2017 Asymptotic analysis of symmetric functions. Zbl 1395.60028Götze, F.; Naumov, A.; Ulyanov, V. 3 2017 Exact upper bounds for the number of the polynomials with given discriminants. Zbl 1435.11097Bernik, Vasili; Budarina, Natalia; Götze, Friedrich 3 2017 Distribution of linear statistics of singular values of the product of random matrices. Zbl 1390.60031Götze, Friedrich; Naumov, Alexey; Tikhomirov, Alexander 3 2017 On algebraic integers in short intervals and near smooth curves. Zbl 1391.11082Götze, Friedrich; Gusakova, Anna 2 2017 Integral polynomials with small discriminants and resultants. Zbl 1339.11073Beresnevich, Victor; Bernik, Vasili; Götze, Friedrich 9 2016 Optimal bounds for convergence of expected spectral distributions to the semi-circular law. Zbl 1338.60014Götze, F.; Tikhomirov, A. 7 2016 On points with algebraically conjugate coordinates close to smooth curves. Zbl 1375.11058Bernik, Vasilii; Götze, Friedrich; Gusakova, A. 5 2016 Arak’s inequalities for concentration functions and the Littlewood-Offord problem. Zbl 1360.60041Götze, F.; Eliseeva, Yu. S.; Zaitsev, A. Yu. 4 2016 Discriminant and root separation of integral polynomials. Zbl 1354.60058Götze, F.; Zaporozhets, D. 3 2016 Regularized distributions and entropic stability of Cramer’s characterization of the normal law. Zbl 1387.60020Bobkov, S. G.; Chistyakov, G. P.; Götze, F. 1 2016 Local semicircle law under weak moment conditions. Zbl 1352.15039Götze, F.; Naumov, A. A.; Tikhomirov, A. N.; Timushev, D. A. 1 2016 Estimates for the concentration functions in the Littlewood-Offord problem. Zbl 1332.15093Eliseeva, Yu. S.; Götze, F.; Zaitsev, A. Yu. 7 2015 Asymptotic spectra of matrix-valued functions of independent random matrices and free probability. Zbl 1331.60019Götze, F.; Kösters, H.; Tikhomirov, A. 7 2015 Distribution of real algebraic numbers of arbitrary degree in short intervals. Zbl 1334.11058Bernik, V. I.; Götze, F. 7 2015 On minimal singular values of random matrices with correlated entries. Zbl 1348.15023Götze, F.; Naumov, A.; Tikhomirov, A. 5 2015 Limit theorems for two classes of random matrices with dependent entries. Zbl 1314.60026Götze, F.; Naumov, A. A.; Tikhomirov, A. N. 4 2015 On a generalization of the elliptic law for random matrices. Zbl 1371.60019Götze, F.; Naumov, A.; Tikhomirov, A. 3 2015 Correlations between real conjugate algebraic numbers. Zbl 1437.11092Götze, F.; Kaliada, D.; Zaporozhets, D. N. 1 2015 On regular systems of algebraic \(p\)-adic numbers of arbitrary degree in small cylinders. Zbl 1388.11038Budarina, N. V.; Götze, F. 1 2015 Berry-Esseen bounds in the entropic central limit theorem. Zbl 1307.60011Bobkov, Sergey G.; Chistyakov, Gennadiy P.; Götze, Friedrich 15 2014 Fisher information and the central limit theorem. Zbl 1372.60018Bobkov, Sergey G.; Chistyakov, Gennadiy P.; Götze, Friedrich 14 2014 Local universality of repulsive particle systems and random matrices. Zbl 1301.60009Götze, Friedrich; Venker, Martin 8 2014 The asymptotic number of integral cubic polynomials with bounded heights and discriminants. Zbl 1322.11078Kaliada, Dzianis; Götze, Friedrich; Kukso, Olga 7 2014 Fisher information and convergence to stable laws. Zbl 1315.60031Bobkov, S. G.; Chistyakov, G. P.; Götze, F. 5 2014 Explicit rates of approximation in the CLT for quadratic forms. Zbl 1290.60021Götze, Friedrich; Zaitsev, Andrei Yu. 5 2014 On algebraic points in the plane near smooth curves. Zbl 1297.11078Bernik, Vasilii; Götze, Friedrich; Kukso, Olga 3 2014 Radial spacing distributions from planar point sets. Zbl 1341.52039Baake, M.; Götze, F.; Huck, C.; Jakobi, T. 1 2014 On the asymptotic distribution of singular values of powers of random matrices. Zbl 1309.15051Alexeev, N. V.; Götze, F.; Tikhomirov, A. N. 1 2014 Rate of convergence and Edgeworth-type expansion in the entropic central limit theorem. Zbl 1296.60051Bobkov, Sergey G.; Chistyakov, Gennadiy P.; Götze, Friedrich 13 2013 Asymptotic expansions in the CLT in free probability. Zbl 1282.46059Chistyakov, G. P.; Götze, F. 6 2013 Distance between conjugate algebraic numbers in clusters. Zbl 1284.11051Budarina, N. V.; Goetze, F. 5 2013 Distribution of algebraic numbers and metric theory of Diophantine approximation. Zbl 1316.11063Bernik, V.; Beresnevich, V.; Götze, F.; Kukso, O. 5 2013 Convergence to stable laws in relative entropy. Zbl 1288.60055Bobkov, S. G.; Chistyakov, G. P.; Götze, F. 3 2013 Stability problems in Cramér-type characterization in case of i.i.d. summands. Zbl 1303.60015Bobkov, S. G.; Chistyakov, G. P.; Götze, F. 2 2013 On the rate of convergence to the semi-circular law. Zbl 1274.60020Götze, Friedrich; Tikhomirov, Alexandre 2 2013 Free infinitely divisible approximations of \(n\)-fold free convolutions. Zbl 1277.46032Chistyakov, Gennadii; Götze, Friedrich 1 2013 Entropic instability of Cramer’s characterization of the normal law. Zbl 1371.60005Bobkov, S. G.; Chistyakov, G. P.; Götze, F. 6 2012 Bounds for characteristic functions in terms of quantiles and entropy. Zbl 1258.60022Bobkov, Sergey G.; Chistyakov, Gennadiy P.; Götze, Friedrich 5 2012 Resampling fewer than \(n\) observations: gains, losses, and remedies for losses. Zbl 1373.62173Bickel, P. J.; Götze, F.; van Zwet, W. R. 4 2012 Birth of a strongly connected giant in an inhomogeneous random digraph. Zbl 1252.05196Bloznelis, Mindaugas; Götze, Friedrich; Jaworski, Jerzy 3 2012 Regular systems of real algebraic numbers of third degree in small intervals. Zbl 1345.11047Bernik, Vasilii; Götze, Friedrich; Kukso, Olga 1 2012 On the distribution of complex roots of random polynomials with heavy-tailed coefficients. Zbl 1266.60095Götze, F.; Zaporozhets, D. 1 2012 The arithmetic of distributions in free probability theory. Zbl 1239.46046Chistyakov, Gennadii P.; Götze, Friedrich 20 2011 Non-uniform bounds in local limit theorems in case of fractional moments. I. Zbl 1239.60016Bobkov, S. G.; Chistyakov, G. P.; Götze, F. 6 2011 Non-uniform bounds in local limit theorems in case of fractional moments. II. Zbl 1307.60010Bobkov, S. G.; Chistyakov, G. P.; Götze, F. 3 2011 Estimates for the rate of strong approximation in Hilbert space. Zbl 1235.60028Götze, F.; Zaitsev, A. Yu. 3 2011 Uniform rates of approximation by short asymptotic expansions in the CLT for quadratic forms. Zbl 1290.60020Götze, F.; Zaitsev, A. Yu. 2 2011 Freeness of linear and quadratic forms in von Neumann algebras. Zbl 1373.46061Chistyakov, G. P.; Götze, F.; Lehner, F. 2 2011 The circular law for random matrices. Zbl 1203.60010Götze, Friedrich; Tikhomirov, Alexander 55 2010 Asymptotic distribution of singular values of powers of random matrices. Zbl 1208.60021Alexeev, N.; Götze, F.; Tikhomirov, A. 20 2010 The distribution of close conjugate algebraic numbers. Zbl 1206.11091Beresnevich, Victor; Bernik, Vasili; Götze, Friedrich 20 2010 On the singular spectrum of powers and products of random matrices. Zbl 1211.60003Alexeev, N. V.; Götze, F.; Tikhomirov, A. N. 12 2010 On concentration of empirical measures and convergence to the semi-circle law. Zbl 1247.60010Bobkov, S. G.; Götze, F.; Tikhomirov, A. N. 11 2010 Simultaneous approximations of zero by an integral polynomial its derivative, and small values of discriminants. Zbl 1267.11079Beresnevich, V. V.; Bernik, V. I.; Götze, F. 6 2010 Concentration of empirical distribution functions with applications to non-i.i.d. models. Zbl 1207.62106Bobkov, S. G.; Götze, F. 4 2010 Rates of approximation in the multidimensional invariance principle for sums of i.i.d. random vectors with finite moments. Zbl 1288.60041Götze, F.; Zaitsev, A. Yu. 3 2010 On the distribution of the values of the resultants of integral polynomials. Zbl 1267.11026Beresnevich, V. V.; Bernik, V. I.; Götze, Friedrich 2 2010 On the second-order correlation function of the characteristic polynomial of a Hermitian Wigner matrix. Zbl 1193.15035Götze, F.; Kösters, H. 11 2009 Bounds for the rate of strong approximation in the multidimensional invariance principle. Zbl 1196.60053Götze, F.; Zaitsev, A. Yu. 6 2009 The rate of convergence of spectra of sample covariance matrices. Zbl 1210.60013Götze, F.; Tikhomirov, A. N. 4 2009 Hardy type inequalities via Riccati and Sturm-Liouville equations. Zbl 1173.26319Bobkov, Sergey; Götze, Friedrich 2 2009 On concentration of high-dimensional matrices with randomly signed entries. Zbl 1288.60004Bobkov, S. G.; Götze, F.; Tikhomirov, A. N. 1 2009 Limit theorems in free probability theory. I. Zbl 1157.46037Chistyakov, G. P.; Götze, F. 17 2008 Lower bounds for the number of integral polynomials with given order of discriminants. Zbl 1222.11096Bernik, Vasili; Götze, Friedrich; Kukso, Olga 13 2008 On the divisibility of the discriminant of an integral polynomial by prime powers. Zbl 1228.11111Bernik, V.; Götze, F.; Kukso, O. 7 2008 Limit correlation functions for fixed trace random matrix ensembles. Zbl 1165.82016Götze, Friedrich; Gordin, Mikhail 5 2008 Limit theorems in free probability theory II. Zbl 1148.46035Chistyakov, Gennadii P.; Götze, Friedrich 5 2008 Concentration inequalities and limit theorems for randomized sums. Zbl 1111.60014Bobkov, Sergey G.; Götze, Friedrich 15 2007 Limit theorems for spectra of random matrices with martingale structure. Zbl 1118.15022Götze, F.; Tikhomirov, A. N. 8 2007 Limit correlation functions at zero for fixed trace random matrix ensembles. Zbl 1153.60026Götze, F.; Gordin, M. I.; Levina, A. 4 2007 Bad-approximable points and distribution of discriminants of the product of linear integer polynomials. Zbl 1236.11065Bernik, V.; Götze, F.; Kukso, O. 3 2007 Rate of convergence to the semi-circle law for the deformed Gaussian unitary Ensemble. Zbl 1155.15027Götze, Friedrich; Tikhomirov, Alexander N.; Timushev, Dmitry A. 3 2007 Asymptotic expansion in the central limit theorem for quadratic forms. Zbl 1123.60013Götze, F.; Tikhomirov, A.; Yurchenko, V. 3 2007 Independence of linear forms with random coefficients. Zbl 1105.62052Chistyakov, G. P.; Götze, F. 3 2007 Non-uniform bounds for short asymptotic expansions in the CLT for balls in a Hilbert space. Zbl 1113.60011Bogatyrev, S. A.; Götze, F.; Ulyanov, V. V. 2 2006 The rate of convergence for spectra of GUE and LUE matrix ensembles. Zbl 1108.60014Götze, Friedrich; Tikhomirov, Alexander 17 2005 Asymptotic expansions in non-central limit theorems for quadratic forms. Zbl 1089.60017Götze, F.; Tikhomirov, A. N. 4 2005 Lattice point problems and values of quadratic forms. Zbl 1090.11063Götze, Friedrich 22 2004 Limit distributions of Studentized means. Zbl 1056.60020Chistyakov, G. P.; Götze, F. 19 2004 Rate of convergence in probability to the Marchenko-Pastur law. Zbl 1049.60018Götze, Friedrich; Tikhomirov, Alexander 17 2004 Limit theorems for spectra of positive random matrices under dependence. Zbl 1075.60017Götze, F.; Tikhomirov, A. 5 2004 Approximation of convolutions by accompanying laws without centering. Zbl 1077.60004Götze, F.; Zaitsev, A. Yu. 2 2004 Distribution of the shape of Markovian random words. Zbl 1103.60011Chistyakov, G. P.; Götze, F. 2 2004 On standard normal convergence of the multivariate Student \(t\)-statistic for symmetric random vectors. Zbl 1056.62013Giné, Evarist; Götze, Friedrich 1 2004 Limiting distributions of theta series on Siegel half-spaces. Zbl 1046.11025Götze, F.; Gordin, M. 1 2004 Rate of convergence to the semi-circular law. Zbl 1031.60019Götze, F.; Tikhomirov, A. 28 2003 ...and 63 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 1,172 Authors 87 Götze, Friedrich W. 34 Bobkov, Sergey Germanovich 23 Bentkus, Vidmants-Kastytis 23 Tikhomirov, Alexander Nikolaevich 22 Chistyakov, Gennadiy P. 17 Shao, Qi-Man 16 Zaitsev, Andrei Yu. 15 Gozlan, Nathael 14 Jing, Bingyi 14 Wu, Liming 13 Bernik, Vasiliĭ Ivanovich 13 Lahiri, Soumendra Nath 13 Roberto, Cyril 13 Zhou, Wang 12 Wang, Qiying 11 Erdős, László 11 Naumov, Alekseĭ Aleksandrovich 11 Peccati, Giovanni 10 Budarina, Natalia Viktorovna 10 Chafaï, Djalil 10 Račkauskas, Alfredas Yurgevich 10 Schnelli, Kevin 9 Bloznelis, Mindaugas 9 Bouzebda, Salim 9 Guillin, Arnaud 9 Mason, David M. 9 Politis, Dimitris Nicolas 9 Wang, Feng-Yu 8 Adamczak, Radosław 8 Bai, Zhi-Dong 8 Houdré, Christian 8 Kaliada, Dzianis 8 Ma, Yutao 8 Nourdin, Ivan 8 Pan, Guangming 8 Pang, Tianxiao 8 Paulauskas, Vygantas Ionovič 8 Samson, Paul-Marie 8 Vu, Van H. 7 Bao, Zhigang 7 Bose, Arup 7 Fathi, Max 7 Forrester, Peter J. 7 Kösters, Holger 7 Lin, Zhengyan 7 Maesono, Yoshihiko 7 O’Rourke, Sean D. 7 Tetali, Prasad 7 Ul’yanov, Vladimir Vasil’evich 7 Yau, Horng-Tzer 7 Zegarlinski, Boguslaw 6 Aistleitner, Christoph 6 Bickel, Peter John 6 Bolley, François 6 Čiginas, Andrius 6 Csörgő, Miklós 6 Gentil, Ivan 6 Gusakova, Anna Grigorevna 6 Hall, Peter Gavin 6 Liu, Dangzheng 6 Liu, Weidong 6 Tao, Terence 6 Toscani, Giuseppe 6 Yin, Jun 6 Zaporozhets, Dmitry 6 Zhang, Zhengliang 5 Barthe, Franck 5 Bertail, Patrice 5 Fukuyama, Katusi 5 Gaunt, Robert Edward 5 Hipp, Christian 5 Jensen, Jens Ledet 5 Lee, Ji Oon 5 O’Donnell, Hugh 5 Privault, Nicolas 5 Reinert, Gesine D. 5 Röllin, Adrian 5 Swan, Yvik C. 4 Akemann, Gernot 4 Berkes, István 4 Bhattacharya, Rabi N. 4 Bordenave, Charles 4 Borovskikh, Yuri V. 4 Boufoussi, Brahim 4 Bühlmann, Peter 4 Capitaine, Mireille 4 Cattiaux, Patrick 4 Clémençon, Stéphan 4 Cook, Nicholas A. 4 Eichelsbacher, Peter 4 Fan, Xiequan 4 Gonçalves, Sílvia 4 Gribkova, Nadezhda V. 4 Janssen, Arnold 4 Ledoux, Michel 4 Lee, Stephen Man Sing 4 Martsynyuk, Yuliya V. 4 Miao, Yu 4 Miclo, Laurent 4 Nasari, Masoud M. ...and 1,072 more Authors all top 5 Cited in 225 Serials 62 Probability Theory and Related Fields 56 The Annals of Probability 42 The Annals of Statistics 41 Bernoulli 39 Journal of Multivariate Analysis 38 Lithuanian Mathematical Journal 36 Journal of Functional Analysis 35 Statistics & Probability Letters 35 Journal of Theoretical Probability 27 Journal of Statistical Planning and Inference 27 Stochastic Processes and their Applications 25 Journal of Mathematical Sciences (New York) 23 Annales de l’Institut Henri Poincaré. 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Académie des Sciences, Paris 4 International Journal of Number Theory 4 Frontiers of Mathematics in China 4 Science China. Mathematics 3 Computers & Mathematics with Applications 3 Metrika 3 Studia Mathematica 3 Mathematics of Computation 3 Acta Mathematica 3 Inventiones Mathematicae 3 Ricerche di Matematica 3 Acta Mathematicae Applicatae Sinica. English Series 3 Random Structures & Algorithms 3 Vestnik St. Petersburg University. Mathematics 3 Applied Mathematics. Series B (English Edition) 3 Statistical Papers 3 Electronic Communications in Probability 3 The Econometrics Journal 3 Journal of the Australian Mathematical Society 3 Journal of Physics A: Mathematical and Theoretical 3 Journal of Statistical Theory and Practice 2 The Canadian Journal of Statistics 2 Mathematical Notes 2 Acta Arithmetica 2 Biometrical Journal 2 Duke Mathematical Journal 2 Glasgow Mathematical Journal 2 Journal für die Reine und Angewandte Mathematik 2 Journal of Soviet Mathematics 2 Mathematische Nachrichten 2 Mathematika 2 Scandinavian Actuarial Journal 2 Stochastic Analysis and Applications 2 Applied Mathematics Letters 2 Journal of the American Mathematical Society ...and 125 more Serials all top 5 Cited in 46 Fields 771 Probability theory and stochastic processes (60-XX) 447 Statistics (62-XX) 135 Linear and multilinear algebra; matrix theory (15-XX) 80 Number theory (11-XX) 76 Functional analysis (46-XX) 58 Real functions (26-XX) 51 Statistical mechanics, structure of matter (82-XX) 43 Numerical analysis (65-XX) 37 Combinatorics (05-XX) 34 Partial differential equations (35-XX) 34 Operator theory (47-XX) 26 Measure and integration (28-XX) 22 Dynamical systems and ergodic theory (37-XX) 22 Global analysis, analysis on manifolds (58-XX) 20 Information and communication theory, circuits (94-XX) 16 Harmonic analysis on Euclidean spaces (42-XX) 14 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 13 Difference and functional equations (39-XX) 11 Quantum theory (81-XX) 10 Special functions (33-XX) 10 Differential geometry (53-XX) 8 Calculus of variations and optimal control; optimization (49-XX) 8 Convex and discrete geometry (52-XX) 8 Operations research, mathematical programming (90-XX) 8 Biology and other natural sciences (92-XX) 7 Potential theory (31-XX) 6 Ordinary differential equations (34-XX) 5 Topological groups, Lie groups (22-XX) 4 History and biography (01-XX) 4 Functions of a complex variable (30-XX) 4 Approximations and expansions (41-XX) 4 Computer science (68-XX) 4 Mechanics of particles and systems (70-XX) 3 Field theory and polynomials (12-XX) 3 Abstract harmonic analysis (43-XX) 2 Order, lattices, ordered algebraic structures (06-XX) 2 Algebraic geometry (14-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Integral transforms, operational calculus (44-XX) 2 Fluid mechanics (76-XX) 1 General and overarching topics; collections (00-XX) 1 Mathematical logic and foundations (03-XX) 1 Group theory and generalizations (20-XX) 1 Geometry (51-XX) 1 Manifolds and cell complexes (57-XX) 1 Geophysics (86-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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