Bulletin of the American Mathematical Society

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Book Information:

Authors: Jinho Baik, Percy Deift and Toufic Suidan
Title: Combinatorics and random matrix theory
Additional book information: Graduate Studies in Mathematics, Vol. 172, American Mathematical Society, Providence, RI, 2016, xi+461 pp., ISBN 978-0-8218-4841-8

Authors: L. Erdős and H. T. Yau
Title: Dynamical approach to random matrix theory
Additional book information: Courant Lecture Notes in Mathematics, Vol. 28, American Mathematical Society, Providence, RI, 2016, ix+226 pp., ISBN 978-1-4704-3648-3

D. Bakry and Michel Émery, Diffusions hypercontractives, Séminaire de probabilités, XIX, 1983/84, Lecture Notes in Math., vol. 1123, Springer, Berlin, 1985, pp. 177–206 (French). MR 889476, DOI 10.1007/BFb0075847

Jinho Baik, Percy Deift, and Kurt Johansson, On the distribution of the length of the longest increasing subsequence of random permutations, J. Amer. Math. Soc. 12 (1999), no. 4, 1119–1178. MR 1682248, DOI 10.1090/S0894-0347-99-00307-0

Jinho Baik, Percy Deift, and Toufic Suidan, Combinatorics and random matrix theory, Graduate Studies in Mathematics, vol. 172, American Mathematical Society, Providence, RI, 2016. MR 3468920, DOI 10.1090/gsm/172

Sourav Chatterjee, A generalization of the Lindeberg principle, Ann. Probab. 34 (2006), no. 6, 2061–2076. MR 2294976, DOI 10.1214/009117906000000575

P. A. Deift, Orthogonal polynomials and random matrices: a Riemann-Hilbert approach, Courant Lecture Notes in Mathematics, vol. 3, New York University, Courant Institute of Mathematical Sciences, New York; American Mathematical Society, Providence, RI, 1999. MR 1677884

Freeman J. Dyson, A Brownian-motion model for the eigenvalues of a random matrix, J. Mathematical Phys. 3 (1962), 1191–1198. MR 148397, DOI 10.1063/1.1703862

László Erdős, Benjamin Schlein, and Horng-Tzer Yau, Universality of random matrices and local relaxation flow, Invent. Math. 185 (2011), no. 1, 75–119. MR 2810797, DOI 10.1007/s00222-010-0302-7

László Erdős and Horng-Tzer Yau, A dynamical approach to random matrix theory, Courant Lecture Notes in Mathematics, vol. 28, Courant Institute of Mathematical Sciences, New York; American Mathematical Society, Providence, RI, 2017. MR 3699468

Ira M. Gessel, Symmetric functions and P-recursiveness, J. Combin. Theory Ser. A 53 (1990), no. 2, 257–285. MR 1041448, DOI 10.1016/0097-3165(90)90060-A

Kurt Johansson, Universality of the local spacing distribution in certain ensembles of Hermitian Wigner matrices, Comm. Math. Phys. 215 (2001), no. 3, 683–705. MR 1810949, DOI 10.1007/s002200000328

J. W. Lindeberg, Eine neue Herleitung des Exponentialgesetzes in der Wahrscheinlichkeitsrechnung, Math. Z. 15 (1922), no. 1, 211–225 (German). MR 1544569, DOI 10.1007/BF01494395

B. F. Logan and L. A. Shepp, A variational problem for random Young tableaux, Advances in Math. 26 (1977), no. 2, 206–222. MR 1417317, DOI 10.1016/0001-8708(77)90030-5

G. de B. Robinson, On the Representations of the Symmetric Group, Amer. J. Math. 60 (1938), no. 3, 745–760. MR 1507943, DOI 10.2307/2371609

C. Schensted, Longest increasing and decreasing subsequences, Canadian J. Math. 13 (1961), 179–191. MR 121305, DOI 10.4153/CJM-1961-015-3

Alexander Soshnikov, Universality at the edge of the spectrum in Wigner random matrices, Comm. Math. Phys. 207 (1999), no. 3, 697–733. MR 1727234, DOI 10.1007/s002200050743

Terence Tao and Van Vu, Random matrices: universality of local eigenvalue statistics, Acta Math. 206 (2011), no. 1, 127–204. MR 2784665, DOI 10.1007/s11511-011-0061-3

Craig A. Tracy and Harold Widom, Level-spacing distributions and the Airy kernel, Comm. Math. Phys. 159 (1994), no. 1, 151–174. MR 1257246

Stanislaw M. Ulam, Monte Carlo calculations in problems of mathematical physics, Modern mathematics for the engineer: Second series, McGraw-Hill, New York, 1961, pp. 261–281. MR 0129165

A. M. Veršik and S. V. Kerov, Asymptotic behavior of the Plancherel measure of the symmetric group and the limit form of Young tableaux, Dokl. Akad. Nauk SSSR 233 (1977), no. 6, 1024–1027 (Russian). MR 0480398

Eugene P. Wigner, Characteristic vectors of bordered matrices with infinite dimensions, Ann. of Math. (2) 62 (1955), 548–564. MR 77805, DOI 10.2307/1970079

• D. Bakry and Michel Émery, Diffusions hypercontractives, Séminaire de probabilités, XIX, 1983/84, Lecture Notes in Math., vol. 1123, Springer, Berlin, 1985, pp. 177–206 (French). MR 889476, DOI 10.1007/BFb0075847
• Jinho Baik, Percy Deift, and Kurt Johansson, On the distribution of the length of the longest increasing subsequence of random permutations, J. Amer. Math. Soc. 12 (1999), no. 4, 1119–1178. MR 1682248, DOI 10.1090/S0894-0347-99-00307-0
• Jinho Baik, Percy Deift, and Toufic Suidan, Combinatorics and random matrix theory, Graduate Studies in Mathematics, vol. 172, American Mathematical Society, Providence, RI, 2016. MR 3468920
• Sourav Chatterjee, A generalization of the Lindeberg principle, Ann. Probab. 34 (2006), no. 6, 2061–2076. MR 2294976, DOI 10.1214/009117906000000575
• P. A. Deift, Orthogonal polynomials and random matrices: a Riemann-Hilbert approach, Courant Lecture Notes in Mathematics, vol. 3, New York University, Courant Institute of Mathematical Sciences, New York; American Mathematical Society, Providence, RI, 1999. MR 1677884
• Freeman J. Dyson, A Brownian-motion model for the eigenvalues of a random matrix, J. Mathematical Phys. 3 (1962), 1191–1198. MR 148397, DOI 10.1063/1.1703862
• László Erdős, Benjamin Schlein, and Horng-Tzer Yau, Universality of random matrices and local relaxation flow, Invent. Math. 185 (2011), no. 1, 75–119. MR 2810797, DOI 10.1007/s00222-010-0302-7
• László Erdős and Horng-Tzer Yau, A dynamical approach to random matrix theory, Courant Lecture Notes in Mathematics, vol. 28, Courant Institute of Mathematical Sciences, New York; American Mathematical Society, Providence, RI, 2017. MR 3699468
• Ira M. Gessel, Symmetric functions and P-recursiveness, J. Combin. Theory Ser. A 53 (1990), no. 2, 257–285. MR 1041448, DOI 10.1016/0097-3165(90)90060-A
• Kurt Johansson, Universality of the local spacing distribution in certain ensembles of Hermitian Wigner matrices, Comm. Math. Phys. 215 (2001), no. 3, 683–705. MR 1810949, DOI 10.1007/s002200000328
• J. W. Lindeberg, Eine neue Herleitung des Exponentialgesetzes in der Wahrscheinlichkeitsrechnung, Math. Z. 15 (1922), no. 1, 211–225 (German). MR 1544569, DOI 10.1007/BF01494395
• B. F. Logan and L. A. Shepp, A variational problem for random Young tableaux, Advances in Math. 26 (1977), no. 2, 206–222. MR 1417317, DOI 10.1016/0001-8708(77)90030-5
• G. de B. Robinson, On the representations of the symmetric group, Amer. J. Math. 60 (1938), no. 3, 745–760. MR 1507943, DOI 10.2307/2371609
• C. Schensted, Longest increasing and decreasing subsequences, Canad. J. Math. 13 (1961), 179–191. MR 0121305, DOI 10.4153/CJM-1961-015-3
• Alexander Soshnikov, Universality at the edge of the spectrum in Wigner random matrices, Comm. Math. Phys. 207 (1999), no. 3, 697–733. MR 1727234, DOI 10.1007/s002200050743
• Terence Tao and Van Vu, Random matrices: universality of local eigenvalue statistics, Acta Math. 206 (2011), no. 1, 127–204. MR 2784665, DOI 10.1007/s11511-011-0061-3
• Craig A. Tracy and Harold Widom, Level-spacing distributions and the Airy kernel, Comm. Math. Phys. 159 (1994), no. 1, 151–174. MR 1257246
• Stanislaw M. Ulam, Monte Carlo calculations in problems of mathematical physics, Modern Mathematics for the Engineer: Second Series, McGraw-Hill, New York, 1961, pp. 261–281. MR 0129165
• A. M. Veršik and S. V. Kerov, Asymptotic behavior of the Plancherel measure of the symmetric group and the limit form of Young tableaux, Dokl. Akad. Nauk SSSR 233 (1977), no. 6, 1024–1027 (Russian). MR 0480398
• Eugene P. Wigner, Characteristic vectors of bordered matrices with infinite dimensions, Ann. of Math. (2) 62 (1955), 548–564. MR 0077805, DOI 10.2307/1970079