The authors consider the length, $ l_N $, of the longest increasing subsequence of a
random permutation of $ N $ numbers. The main result in this paper is a proof that the …

Random matrix theory is a wide and growing field with a variety of concepts, results, and
techniques and a vast range of applications in mathematics and the related sciences. The …

We consider asymptotics of orthogonal polynomials with respect to weights w (x) dx= e− Q
(x) dx on the real line, where Q (x)= Σ qk xk, q2m> 0, denotes a polynomial of even order …

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The analysis of orthogonal polynomials associated with general weights was a major theme
in classical analysis in the twentieth century, and undoubtedly will continue to grow in …

This book describes the theory and applications of discrete orthogonal polynomials--
polynomials that are orthogonal on a finite set. Unlike other books, Discrete Orthogonal …

This paper is concerned with Hermite-Padé rational approximants of analytic functions and
their connection with multiple orthogonal polynomial ensembles of random matrices. Results …

We study the partition function from random matrix theory using a well-known connection to
orthogonal polynomials, and a recently developed Riemann-Hilbert approach to the …

We survey a number of models from physics, statistical mechanics, probability theory and
combinatorics, which are each described in terms of an orthogonal polynomial ensemble …

Abstract The Tracy-Widom distribution functions involve integrals of a Painlevé II function
starting from positive infinity. In this paper, we express the Tracy-Widom distribution …