@incollection{SB_1999-2000__42__411_0,
author = {van Moerbeke, Pierre},
title = {Random matrices and permutations, matrix integrals and integrable systems},
booktitle = {S\'eminaire Bourbaki : volume 1999/2000, expos\'es 865-879},
series = {Ast\'erisque},
note = {talk:879},
pages = {411--433},
year = {2002},
publisher = {Soci\'et\'e math\'ematique de France},
number = {276},
mrnumber = {1886768},
zbl = {0995.15019},
language = {en},
url = {https://www.numdam.org/item/SB_1999-2000__42__411_0/}
}
TY - CHAP AU - van Moerbeke, Pierre TI - Random matrices and permutations, matrix integrals and integrable systems BT - Séminaire Bourbaki : volume 1999/2000, exposés 865-879 AU - Collectif T3 - Astérisque N1 - talk:879 PY - 2002 SP - 411 EP - 433 IS - 276 PB - Société mathématique de France UR - https://www.numdam.org/item/SB_1999-2000__42__411_0/ LA - en ID - SB_1999-2000__42__411_0 ER -
%0 Book Section %A van Moerbeke, Pierre %T Random matrices and permutations, matrix integrals and integrable systems %B Séminaire Bourbaki : volume 1999/2000, exposés 865-879 %A Collectif %S Astérisque %Z talk:879 %D 2002 %P 411-433 %N 276 %I Société mathématique de France %U https://www.numdam.org/item/SB_1999-2000__42__411_0/ %G en %F SB_1999-2000__42__411_0
van Moerbeke, Pierre. Random matrices and permutations, matrix integrals and integrable systems, dans Séminaire Bourbaki : volume 1999/2000, exposés 865-879, Astérisque, no. 276 (2002), Exposé no. 879, 23 p.. https://www.numdam.org/item/SB_1999-2000__42__411_0/
[1] and : Symmetric random matrices and the Pfaff Lattice, to appear in: Annals of Mathematics, sept 2000 (solv-int/9903009) and The Hermitian, symmetric and symplectic ensembles and PDE's (math. -phys./009001). | MR
[2] and : The spectrum of coupled random matrices, Annals of Mathematics, 149, 921-976 (1999). | Zbl | MR
[3] and : Integrals over classical groups, random permutations, Toda and Toeplitz lattices, Comm. Pure Appl. Math. (2000) (math.CO/9912143). | Zbl | MR
[4] , and : Random matrices, vertex operators and the Virasoro algebra, Phys. Lett. A 208, 101-112, (1995). And Random matrices, Virasoro algebras and non-commutative KP, Duke Math. J. 94, 379-431 (1998). | Zbl | MR
[5] and : Longest increasing subsequences: From patience sorting to the Baik-Deift-Johansson theorem, Bull. Am. Math. Soc. (new series) 36 (4), 413-432 (1999). | Zbl | MR
[6] , and : On the distribution of the length of the longest increasing subsequence of random permutations, Math. Archive, Journal Amer. Math. Soc. 12, 1119-1178 (1999) (math. CO/9810105). | Zbl | MR
[7] and : Algebraic aspects of increasing subsequences, (1999), math.CO/9905083
[8] , and : Quantum field theory techniques in graphical enumeration, Adv. Appl. Math. 1, 109-157 (1980). | Zbl | MR
[9] : Representations of symmetric groups and free probability, preprint (1998). | MR
[10] and : Universal scaling of the tail of the density of eigenvalues in random matrix models, Phys. Letters B 268, 21-28 (1991). | MR
[11] , , : A method of integration over matrix variables : II, J. Phys. A: Math. Gen. 14, 579-586 (1981). | MR
[12] : Chazy classes IX-XII of third-order differential equations, Stud. Appl. Math. 104, 3, 171-228 (2000). | Zbl | MR
[13] , : On the eigenvalues of random matrices J. Appl. Prob., suppl. in honour of Takàcs 31A, 49-61 (1994). | Zbl | MR
[14] and : A combinatorial theorem in geometry, Compositio Math., 2, 463-470 (1935). | JFM | Numdam
[15] , , : The isomonodromy approach to matrix models in quantum gravity, Comm. Math. Phys., 147, 395-430 (1992). | Zbl | MR
[16] : The spectrum edge of random matrix ensembles, Nucl. Phys. B, (1993). | Zbl | MR
[17] : Symmetric functions and -recursiveness, J. of Comb. Theory, Ser A, 53, 257-285 (1990). | Zbl | MR
[18] : A few seedlings of research, Proc. Sixth. Berkeley Symp. Math. Statist. and Probability, Vol. 1, 345-394, University of California Press (1972). | Zbl | MR
[19] : Unitary matrix models and Painlevé III, Mod. Phys. Letters, A 11 3001-3010 (1996). | Zbl | MR
[20] , : The planar approximation, J. Math. Phys. 21, 411-421 (1980). | Zbl | MR
[21] , , and : Density matrix of an impenetrable Bose gas and the fifth Painlevé transcendent, Physica 1D, 80-158 (1980). | MR
[22] : The Longest Increasing Subsequence in a Random Permutation and a Unitary Random Matrix Model, Math. Res. Lett., 5, no. 1-2, 63-82 (1998). | Zbl | MR
[23] and : A variational problem for random Young tableaux, Advances in Math., 26, 206-222 (1977). | Zbl | MR
[24] , , : Universality of random-matrix predictions for the statistics of energy levels Phys. rev. letters 60,1995-1998 (1988). | MR
[25] : Intersection theory on the moduli space of curves and the matrix Airy function, Comm. Math. Phys. 147, 1-23 (1992). | Zbl | MR
[26] : "The Art of Computer programming, Vol III: Searching and Sorting", Addison-Wesley, Reading, MA, 1973. | Zbl | MR
[27] , : A method of integration over matrix variables: IV, J. Phys. I (France) 1, 1093-1108 (1991). | MR
[28] : Random matrices, 2nd ed. Boston: Acad. Press, 1991. | Zbl | MR
[29] , : Correlation functions of random matrix ensembles related to classical orthogonal polynomials, J. Phys. Soc of Japan, 60 3298-3322 (1991). | MR
[30] : On the distribution of spacings between the zeros of the zeta function 48, 273-308 (1987). | Zbl | MR
[31] : Random matrices and random permutations (1999), math.CO/ 9903176 | MR
[32] : On the universality of the level spacing distribution for some ensembles of random matrices, Letters Math. Phys., 25 259-265 (1992). | Zbl | MR
[33] : Topics in Probability on compact Lie groups, Harvard University doctoral dissertation, (1995). 5B
[34] : Increasing subsequences and the classical groups, Elect. J. of Combinatorics, 5, R12 (1998). | Zbl | MR
[35] and : Level-Spacings distribution and the Airy kernel, Commun. Math. Phys., 159, 151-174 (1994). | Zbl | MR
[36] and : Random unitary matrices, permutations and Painlevé (1999), math.CO/9811154 | MR
[37] and : On the distribution of the lengths of the longest monotone subsequences in random words (1999), math.CO/9904042
[38] : Monte Carlo calculations in problems of mathematical physics, in Modern Mathematics for the Engineers, E.F. Beckenbach ed., McGraw-Hill, 261- 281 (1961). | MR
[39] : Integrable lattices: random matrices and permutations, MSRI-volume on Random matrices and exactly solvable models, Eds.: P. Bleher, A. Its, Oxford University press, 2000 (math.CO/00-10). | Zbl
[40] and : Asymptotics of the Plancherel measure of the symmetric group and the limiting form of Young tableaux, Soviet Math. Dokl., 18, 527-531 (1977). | Zbl







