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## UNIFORM ASYMPTOTICS FOR POLYNOMIALS ORTHOGONAL WITH RESPECT TO VARYING EXPONENTIAL WEIGHTS AND APPLICATIONS TO UNIVERSALITY QUESTIONS IN RANDOM MATRIX THEORY

- P. Deift, T. Kriecherbauer, K. Mclaughlin, S. Venakides, Xin Zhou
- Mathematics
- 1 November 1999

We consider asymptotics for orthogonal polynomials with respect to varying exponential weights wn(x)dx = e−nV(x)dx on the line as n ∞. The potentials V are assumed to be real analytic, with… Expand

## Strong asymptotics of orthogonal polynomials with respect to exponential weights

- P. Deift, T. Kriecherbauer, K. Mclaughlin, S. Venakides, Xin Zhou
- Mathematics
- 1 December 1999

We consider asymptotics of orthogonal polynomials with respect to weights w(x)dx= e Q(x) dx on the real line, where Q(x)=∑ 2m k=0 qkx k , q2m> 0, denotes a polynomial of even order with positive… Expand

## New Results on the Equilibrium Measure for Logarithmic Potentials in the Presence of an External Field

- P. Deift, T. Kriecherbauer, K. Mclaughlin
- Mathematics
- 1 December 1998

In this paper we use techniques from the theory of ODEs and also from inverse scattering theory to obtain a variety of results on the regularity and support properties of the equilibrium measure for… Expand

## Strong asymptotics of polynomials orthogonal with respect to Freud weights

- T. Kriecherbauer, K. Mclaughlin
- Mathematics
- 1999

## Discrete orthogonal polynomials: Asymptotics and applications

- J. Baik, T. Kriecherbauer, K. Mclaughlin, P. Miller
- Mathematics
- 2 January 2007

Preface vii Chapter 1. Introduction 1 Chapter 2. Asymptotics of General Discrete Orthogonal Polynomials in the Complex Plane 25 Chapter 3. Applications 49 Chapter 4. An Equivalent Riemann-Hilbert… Expand

## The toda rarefaction problem

- P. Deift, S. Kamvissis, T. Kriecherbauer, Xin Zhou
- Mathematics
- 1996

In the Toda shock problem (see [7], (1 11, [S], and also 131) one considers a driving particle moving with a fixed velocity 2a and impinging on a one-dimensional semi-infinite lattice of particles,… Expand

## Uniform Asymptotics for Polynomials Orthogonal With Respect to a General Class of Discrete Weights and Universality Results for Associated Ensembles

- J. Baik, T. Kriecherbauer, K. Mclaughlin, P. Miller
- Mathematics
- 10 December 2002

This is the full version of "Uniform Asymptotics for Polynomials Orthogonal With Respect to a General Class of Discrete Weights and Universality Results for Associated Ensembles: Announcement of… Expand

## A pedestrian's view on interacting particle systems, KPZ universality and random matrices

- T. Kriecherbauer, J. Krug
- Physics
- 19 March 2008

These notes are based on lectures delivered by the authors at a Langeoog seminar of SFB/TR12 Symmetries and Universality in Mesoscopic Systems to a mixed audience of mathematicians and theoretical… Expand

## Fluctuations of eigenvalues of matrix models and their applications

- T. Kriecherbauer, M. Shcherbina
- Mathematics
- 31 March 2010

We study the expectation of linear eigenvalue statistics of matrix models with any $\beta>0$, assuming that the potential $V$ is a real analytic function and that the corresponding equilibrium… Expand

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