Götze, F.; Tikhomirov, A.; Timushev, D. Rate of convergence for sparse sample covariance matrices. (English) Zbl 07822571 Belomestny, Denis (ed.) et al., Foundations of modern statistics. Festschrift in honor of Vladimir Spokoiny. Selected contributions based on the presentations at the international conference, Berlin, Germany, November 6–8, 2019 and Moscow, Russia, November 30, 2019. Cham: Springer. Springer Proc. Math. Stat. 425, 261-300 (2023). MSC: 62-XX PDFBibTeX XMLCite \textit{F. Götze} et al., Springer Proc. Math. Stat. 425, 261--300 (2023; Zbl 07822571) Full Text: DOI
Götze, F.; Timushev, D. A.; Tikhomirov, A. N. Local Marchenko-Pastur law for sparse rectangular random matrices. (English. Russian original) Zbl 1486.60013 Dokl. Math. 104, No. 3, 332-335 (2021); translation from Dokl. Ross. Akad. Nauk, Mat. Inform. Protsessy Upr. 501, 22-25 (2021). MSC: 60B20 15B52 PDFBibTeX XMLCite \textit{F. Götze} et al., Dokl. Math. 104, No. 3, 332--335 (2021; Zbl 1486.60013); translation from Dokl. Ross. Akad. Nauk, Mat. Inform. Protsessy Upr. 501, 22--25 (2021) Full Text: DOI
Götze, F.; Naumov, A. A.; Tikhomirov, A. N. Local semicircle law under moment conditions: the Stieltjes transform, rigidity, and delocalization. (English. Russian original) Zbl 1426.15056 Theory Probab. Appl. 62, No. 1, 58-83 (2018); translation from Teor. Veroyatn. Primen. 62, No. 1, 72-103 (2017). Reviewer: Zakhar Kabluchko (Münster) MSC: 15B52 60B20 PDFBibTeX XMLCite \textit{F. Götze} et al., Theory Probab. Appl. 62, No. 1, 58--83 (2018; Zbl 1426.15056); translation from Teor. Veroyatn. Primen. 62, No. 1, 72--103 (2017) Full Text: DOI arXiv
Alexeev, Nikita; Tikhomirov, Alexander Singular values distribution of squares of elliptic random matrices and type B Narayana polynomials. (English) Zbl 1390.60026 J. Theor. Probab. 30, No. 3, 1170-1190 (2017). Reviewer: Zakhar Kabluchko (Münster) MSC: 60B20 60F05 15B52 PDFBibTeX XMLCite \textit{N. Alexeev} and \textit{A. Tikhomirov}, J. Theor. Probab. 30, No. 3, 1170--1190 (2017; Zbl 1390.60026) Full Text: DOI arXiv
Götze, F.; Naumov, A. A.; Tikhomirov, A. N.; Timushev, D. A. Local semicircle law under weak moment conditions. (English. Russian original) Zbl 1352.15039 Dokl. Math. 93, No. 3, 248-250 (2016); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 468, No. 1, 12-15 (2016). MSC: 15B52 60B20 15A18 PDFBibTeX XMLCite \textit{F. Götze} et al., Dokl. Math. 93, No. 3, 248--250 (2016; Zbl 1352.15039); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 468, No. 1, 12--15 (2016) Full Text: DOI
Götze, F.; Kösters, H.; Tikhomirov, A. Asymptotic spectra of matrix-valued functions of independent random matrices and free probability. (English) Zbl 1331.60019 Random Matrices Theory Appl. 4, No. 2, Article ID 1550005, 85 p. (2015). MSC: 60B20 46L54 PDFBibTeX XMLCite \textit{F. Götze} et al., Random Matrices Theory Appl. 4, No. 2, Article ID 1550005, 85 p. (2015; Zbl 1331.60019) Full Text: DOI arXiv
Götze, F.; Naumov, A. A.; Tikhomirov, A. N. Limit theorems for two classes of random matrices with dependent entries. (English. Russian original) Zbl 1314.60026 Theory Probab. Appl. 59, No. 1, 23-39 (2015); translation from Teor. Veroyatn. Primen. 59, No. 1, 61-80 (2014). MSC: 60B20 60F05 PDFBibTeX XMLCite \textit{F. Götze} et al., Theory Probab. Appl. 59, No. 1, 23--39 (2015; Zbl 1314.60026); translation from Teor. Veroyatn. Primen. 59, No. 1, 61--80 (2014) Full Text: DOI
Tikhomirov, A. N. Asymptotic distribution of singular values for matrices in a spherical ensemble. (Russian, English) Zbl 1340.15032 Mat. Tr. 16, No. 2, 169-200 (2013); translation in Sib. Adv. Math. 24, No. 4, 282-303 (2014). MSC: 15B52 15A18 60B20 PDFBibTeX XMLCite \textit{A. N. Tikhomirov}, Mat. Tr. 16, No. 2, 169--200 (2013; Zbl 1340.15032); translation in Sib. Adv. Math. 24, No. 4, 282--303 (2014) Full Text: DOI
Tikhomirov, A. N. On asymptotics for the spectrum of the product of two random rectangular matrices. (English. Russian original) Zbl 1236.60011 Sib. Math. J. 52, No. 4, 747-762 (2011); translation from Sib. Mat. Zh. 52, No. 4, 936-954 (2011). Reviewer: Michael Stolz (Bochum) MSC: 60B20 15B52 PDFBibTeX XMLCite \textit{A. N. Tikhomirov}, Sib. Math. J. 52, No. 4, 747--762 (2011; Zbl 1236.60011); translation from Sib. Mat. Zh. 52, No. 4, 936--954 (2011) Full Text: DOI
Alexeev, N.; Götze, F.; Tikhomirov, A. Asymptotic distribution of singular values of powers of random matrices. (English) Zbl 1208.60021 Lith. Math. J. 50, No. 2, 121-132 (2010). MSC: 60F05 15B52 60B20 PDFBibTeX XMLCite \textit{N. Alexeev} et al., Lith. Math. J. 50, No. 2, 121--132 (2010; Zbl 1208.60021) Full Text: DOI arXiv
Bobkov, S. G.; Götze, F.; Tikhomirov, A. N. On concentration of empirical measures and convergence to the semi-circle law. (English) Zbl 1247.60010 J. Theor. Probab. 23, No. 3, 792-823 (2010). Reviewer: Michael Voit (Dortmund) MSC: 60B20 PDFBibTeX XMLCite \textit{S. G. Bobkov} et al., J. Theor. Probab. 23, No. 3, 792--823 (2010; Zbl 1247.60010) Full Text: DOI
Bobkov, S. G.; Götze, F.; Tikhomirov, A. N. On concentration of high-dimensional matrices with randomly signed entries. (English) Zbl 1288.60004 J. Math. Sci., New York 163, No. 4, 328-351 (2009) and Zap. Nauchn. Semin. POMI 364, 32-69 (2009). MSC: 60B20 60E10 60F05 PDFBibTeX XMLCite \textit{S. G. Bobkov} et al., J. Math. Sci., New York 163, No. 4, 328--351 (2009; Zbl 1288.60004) Full Text: DOI
Götze, Friedrich; Tikhomirov, Alexander N.; Timushev, Dmitry A. Rate of convergence to the semi-circle law for the deformed Gaussian unitary Ensemble. (English) Zbl 1155.15027 Cent. Eur. J. Math. 5, No. 2, 305-334 (2007). Reviewer: Costică Moroşanu (Iaşi) MSC: 15B52 60F99 41A60 PDFBibTeX XMLCite \textit{F. Götze} et al., Cent. Eur. J. Math. 5, No. 2, 305--334 (2007; Zbl 1155.15027) Full Text: DOI
Götze, Friedrich; Tikhomirov, Alexander The rate of convergence for spectra of GUE and LUE matrix ensembles. (English) Zbl 1108.60014 Cent. Eur. J. Math. 3, No. 4, 666-704 (2005). MSC: 60F05 15B52 33C45 82B31 PDFBibTeX XMLCite \textit{F. Götze} and \textit{A. Tikhomirov}, Cent. Eur. J. Math. 3, No. 4, 666--704 (2005; Zbl 1108.60014) Full Text: DOI
Götze, Friedrich; Tikhomirov, Alexander Rate of convergence in probability to the Marchenko-Pastur law. (English) Zbl 1049.60018 Bernoulli 10, No. 3, 503-548 (2004). MSC: 60F05 PDFBibTeX XMLCite \textit{F. Götze} and \textit{A. Tikhomirov}, Bernoulli 10, No. 3, 503--548 (2004; Zbl 1049.60018) Full Text: DOI Euclid