Some Open Problems in Random Matrix Theory and the Theory of Integrable Systems. II

Abstract

We describe a list of open problems in random matrix theory and the theory of integrable systems that was presented at the conference Asymptotics in Integrable Systems, Random Matrices and Random Processes and Universality, Centre de Recherches Mathematiques, Montreal, June 7-11, 2015. We also describe progress that has been made on problems in an earlier list presented by the author on the occasion of his 60th birthday in 2005 (see [Deift P., Contemp. Math., Vol. 458, Amer. Math. Soc., Providence, RI, 2008, 419-430, arXiv:0712.0849]).

for Part I see arXiv:0712.0849

References in corpus (7)

• Probability Distribution of the Free Energy of the Continuum Directed Random Polymer in 1+1 dimensions
• Asymptotics in ASEP with Step Initial Condition
• A Fredholm Determinant Representation in ASEP
• Randomly incomplete spectra and intermediate statistics
• Fluctuations of eigenvalues of matrix models and their applications
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Cited by in corpus (8)

• Asymptotics of spectral gaps of quasi-periodic Schrödinger operators
• KdV equation beyond standard assumptions on initial data
• Open Problems for Painlevé Equations
• A geometrical triumvirate of real random matrices
• Statistical properties of eigenvalues of an ensemble of pseudo-Hermitian Gaussian matrices
• The dbar steepest descent method for orthogonal polynomials on the real line with varying weights
• Phase transitions for infinite products of large non-Hermitian random matrices
• Random matrices applications to soft spectra