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]).

arXiv commentfor Part I see arXiv:0712.0849

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Cited by in corpus (25)

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• Products of Many Large Random Matrices and Gradients in Deep Neural Networks
• Almost Periodicity in Time of Solutions of the KdV Equation
• Asymptotics of spectral gaps of quasi-periodic Schrödinger operators
• Invariance of white noise for KdV on the line
• A universal bound on Quantum Chaos from Random Matrix Theory
• Open Problems for Painlevé Equations
• KdV equation beyond standard assumptions on initial data
• A geometrical triumvirate of real random matrices
• Lyapunov exponent, universality and phase transition for products of random matrices
• The Robin problem for the nonlinear Schrödinger equation on the half-line
• Global well-posedness for $H^{-1}(\mathbb{R})$ perturbations of KdV with exotic spatial asymptotics
• Gaussian Determinantal Processes: a new model for directionality in data
• Statistical properties of eigenvalues of an ensemble of pseudo-Hermitian Gaussian matrices
• The Dyson and Coulomb games
• The dbar steepest descent method for orthogonal polynomials on the real line with varying weights
• Local Existence and Uniqueness of Spatially Quasi-Periodic Solutions to the Generalized KdV Equation
• Long-time dynamics of small solutions to 1$d$ cubic nonlinear Schrödinger equations with a trapping potential
• Phase transitions for infinite products of large non-Hermitian random matrices
• The Quasi-Periodic Cauchy Problem for the Generalized Benjamin-Bona-Mahony Equation on the Real Line
• Complexity of Path-Following Methods for the Eigenvalue Problem
• A note on quantum chaology and gamma approximations to eigenvalue spacings for infinite random matrices
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• The Deift Conjecture: A Program to Construct a Counterexample
• A nonlinear stationary phase method for oscillatory Riemann-Hilbert problems