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Expansion of polynomial Lie group integrals in terms of certain maps on surfaces, and factorizations of permutations. (English) Zbl 1360.81176

MSC:
81Q50 Quantum chaos
22E70 Applications of Lie groups to the sciences; explicit representations
20B30 Symmetric groups
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[1] Weingarten D 1978 Asymptotic behavior of group integrals in the limit of infinite rank J. Math. Phys.19 999 · Zbl 0388.28013
[2] Samuel S 1980 U(N) integrals, 1/N, and de Wit-’t Hooft anomalies J. Math. Phys.21 2695
[3] Mello P A 1990 Averages on the unitary group and applications to the problem of disordered conductors J. Phys. A: Math. Gen.23 4061
[4] Brouwer P W and Beenakker C W J 1996 Diagrammatic method of integration over the unitary group, with applications to quantum transport in mesoscopic systems J. Math. Phys.37 4904 · Zbl 0861.22014
[5] Degli Esposti M and Knauf A 2004 On the form factor for the unitary group J. Math. Phys.45 4957 · Zbl 1064.81036
[6] Collins B 2003 Moments and cumulants of polynomial random variables on unitary groups, the Itzykson-Zuber integral, and free probability Int. Math. Res. Not.17 953 · Zbl 1049.60091
[7] Collins B and Śniady P 2006 Integration with respect to the Haar measure on unitary, orthogonal and symplectic group Commun. Math. Phys.264 773 · Zbl 1108.60004
[8] Collins B and Matsumoto S 2009 On some properties of orthogonal Weingarten functions J. Math. Phys.50 113516 · Zbl 1304.22007
[9] Zuber J-B 2008 The large-N limit of matrix integrals over the orthogonal group J. Phys. A: Math. Theor.41 382001 · Zbl 1147.82019
[10] Banica T, Collins B and Schlenker J-M 2011 On polynomial integrals over the orthogonal group J. Comb. Theory A 118 78 · Zbl 1227.05057
[11] Matsumoto S and Novak J 2013 Jucys-Murphy elements and unitary matrix integrals Int. Math. Res. Not.2 362 · Zbl 1312.05143
[12] Zinn-Justin P 2010 Jucys-Murphy elements and Weingarten matrices Lett. Math. Phys.91 119 · Zbl 1283.05269
[13] Matsumoto S 2013 Weingarten calculus for matrix ensembles associated with compact symmetric spaces Random Matrices: Theory Appl.2 1350001 · Zbl 1280.15020
[14] Scott A J 2008 Optimizing quantum process tomography with unitary 2-designs J. Phys. A: Math. Theor.41 055308 · Zbl 1141.81009
[15] Žnidarič M, Pineda C and García-Mata I 2011 Non-Markovian behavior of small and large complex quantum systems Phys. Rev. Lett.107 080404
[16] Cramer M 2012 Thermalization under randomized local Hamiltonians New J. Phys.14 053051
[17] Vinayak and Žnidarič M 2012 Subsystem’s dynamics under random Hamiltonian evolution J. Phys. A: Math. Theor.45 125204 · Zbl 1245.81065
[18] Novaes M 2013 A semiclassical matrix model for quantum chaotic transport J. Phys. A: Math. Theor.46 502002 · Zbl 1298.82062
[19] Novaes M 2015 Semiclassical matrix model for quantum chaotic transport with time-reversal symmetry Ann. Phys.361 51 · Zbl 1360.81177
[20] Novaes M 2014 Elementary derivation of Weingarten functions of classical Lie groups (arXiv:1406.2182v2 [math-ph])
[21] Zinn-Justin P and Zuber J-B 2003 On some integrals over the U(N) unitary group and their large N limit J. Phys. A: Math. Gen.36 3173 · Zbl 1074.82013
[22] Collins B, Guionnet A and Maurel-Segala E 2009 Asymptotics of unitary and orthogonal matrix integrals Adv. Math.222 172 · Zbl 1184.15024
[23] Ginibre J 1965 Statistical ensembles of complex, quaternion, and real matrices J. Math. Phys.6 440 · Zbl 0127.39304
[24] Morris T R 1991 Chequered surfaces and complex matrices Nucl. Phys. B 356 703
[25] ’t Hooft G 1974 A planar diagram theory for strong interactions Nucl. Phys. B 72 461
[26] Bessis D, Itzykson C and Zuber J B 1980 Quantum field theory techniques in graphical enumeration Adv. Appl. Math.1 109 · Zbl 0453.05035
[27] Di Francesco P 2003 Rectangular matrix models and combinatorics of colored graphs Nucl. Phys. B 648 461 · Zbl 1005.82003
[28] Novaes M 2015 Statistics of time delay and scattering correlation functions in chaotic systems. II. Semiclassical approximation J. Math. Phys.56 062109 · Zbl 1322.81049
[29] Bousquet-Mélou M and Schaeffer G 2000 Enumeration of planar constellations Adv. Appl. Math.24 337 · Zbl 0955.05004
[30] Irving J 2009 Minimal transitive factorizations of permutations into cycles Can. J. Math.61 1092 · Zbl 1186.05006
[31] Bouttier J 2011 Matrix integrals and enumeration of maps The Oxford Handbook of Random Matrix Theory ed G Akemann et al (Oxford: Oxford University Press) ch 26
[32] Berkolaiko G and Irving J 2016 Inequivalent factorizations of permutations J. Combin. Theory A 140 1-37 · Zbl 1331.05005
[33] Bóna M and Pittel B 2016 On the cycle structure of the product of random maximal cycles (arXiv:1601.00319v1)
[34] Bernardi O, Morales A, Stanley R and Du R 2014 Separation probabilities for products of permutations Comb. Probab. Comput.23 201 · Zbl 1290.05003
[35] Morales A H and Vassilieva E A 2010 Bijective evaluation of the connection coefficients of the double coset algebra (arXiv:1011.5001v1)
[36] Hanlon P J, Stanley R P and Stembridge J R 1992 Some combinatorial aspects of the spectra of normally distributed random matrices Contemp. Math.138 151 · Zbl 0789.05092
[37] Goulden I P and Jackson D M 1996 Maps in locally orientable surfaces, the double coset algebra, and zonal polynomials Can. J. Math.48 569 · Zbl 0861.05062
[38] Matsumoto S 2011 Jucys-Murphy elements, orthogonal matrix integrals, and Jack measures Ramanujan J.26 69 · Zbl 1233.05214
[39] Berkolaiko G and Kuipers J 2013 Combinatorial theory of the semiclassical evaluation of transport moments I: equivalence with the random matrix approach J. Math. Phys.54 112103 · Zbl 1288.81048
[40] Müller S, Heusler S, Braun P and Haake F 2007 Semiclassical approach to chaotic quantum transport New J. Phys.9 12
[41] Müller S, Heusler S, Braun P, Haake F and Altland A 2005 Periodic-orbit theory of universality in quantum chaos Phys. Rev. E 72 046207
[42] Berkolaiko G and Kuipers J 2013 Combinatorial theory of the semiclassical evaluation of transport moments II: algorithmic approach for moment generating functions J. Math. Phys.54 123505 · Zbl 1288.82053
[43] Novaes M 2012 Semiclassical approach to universality in quantum chaotic transport Europhys. Lett.98 20006
[44] Novaes M 2013 Combinatorial problems in the semiclassical approach to quantum chaotic transport J. Phys. A: Math. Theor.46 095101 · Zbl 1267.81171
[45] Macdonald I G 1995 Symmetric Functions and Hall Polynomials 2nd edn (Oxford: Oxford University Press)
[46] Friedman W A and Mello P A 1985 Marginal distribution of an arbitrary square submatrix of the S-matrix for Dyson’s measure J. Phys. A: Math. Gen.18 425 · Zbl 0572.60025
[47] Życzkowski K and Sommers H-J 2000 Truncations of random unitary matrices J. Phys. A: Math. Gen.33 2045 · Zbl 0957.82017
[48] Neretin Y A 2002 Hua-type integrals over unitary groups and over projective limits of unitary groups Duke Math. J.114 239 · Zbl 1019.43008
[49] Forrester P J 2006 Quantum conductance problems and the Jacobi ensemble J. Phys. A: Math. Gen.39 6861 · Zbl 1092.81069
[50] Fyodorov Y V and Khoruzhenko B A 2007 A few remarks on colour-flavour transformations, truncations of random unitary matrices, Berezin reproducing kernels and Selberg-type integrals J. Phys. A: Math. Theor.40 669 · Zbl 1183.81070
[51] Shen J 2001 On the singular values of Gaussian random matrices Linear Algebr. Appl.326 1 · Zbl 0985.15019
[52] Edelman A and Rao N R 2005 Random matrix theory Acta Numer.14 233 · Zbl 1162.15014
[53] Mehta M L 2004 Random Matrices (New York: Academic) ch 17
[54] Forrester P J and Warnaar S O 2008 The importance of the Selberg integral Bull. Am. Math. Soc.45 489 · Zbl 1154.33002
[55] Khoruzhenko B A, Sommers H-J and Życzkowski K 2010 Truncations of random orthogonal matrices Phys. Rev. E 82 040106
[56] Stanley R P 1999 (Enumerative Combinatorics vol 2) (Cambridge: Cambridge University Press) · Zbl 0928.05001
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