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On the distribution of the length of the longest increasing subsequence of random permutations

- J. Baik, P. Deift, K. Johansson
- Mathematics
- 16 October 1998

Let SN be the group of permutations of 1,2,..., N. If 7r E SN, we say that 7(i1),... , 7F(ik) is an increasing subsequence in 7r if il < i2 < ... < ik and 7r(ii) < 7r(i2) < ...< 7r(ik). Let 1N(r) be… Expand

Eigenvalues of large sample covariance matrices of spiked population models

- J. Baik, J. W. Silverstein
- Mathematics
- 12 August 2004

Phase transition of the largest eigenvalue for nonnull complex sample covariance matrices

- J. Baik, G. B. Arous, S. Péché
- Mathematics
- 1 March 2004

AbstractWe compute the limiting distributions of the largest eigenvalue of a complex Gaussian samplecovariance matrix when both the number of samples and the number of variables in each samplebecome… Expand

Algebraic aspects of increasing subsequences

We present a number of results relating partial Cauchy-Littlewood sums, integrals over the compact classical groups, and increasing subsequences of permutations. These include: integral formulae for… Expand

Limiting Distributions for a Polynuclear Growth Model with External Sources

The purpose of this paper is to investigate the limiting distribution functions for a polynuclear growth model with two external sources which was considered by Prähofer and Spohn. Depending on the… Expand

The Oxford Handbook of Random Matrix Theory

- G. Akemann, J. Baik, P. Francesco
- Mathematics
- 25 September 2011

I INTRODUCTION II PROPERTIES OF RANDOM MATRIX THEORY III APPLICATIONS OF RANDOM MATRIX THEORY

Symmetrized Random Permutations

Selecting N random points in a unit square corresponds to selecting a random permutation. By putting 5 types of symmetry restrictions on the points, we obtain subsets of permutations : involutions,… Expand

The asymptotics of monotone subsequences of involutions

We compute the limiting distributions of the lengths of the longest monotone subsequences of random (signed) involutions with or without conditions on the number of fixed points (and negated points)… Expand

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

Discrete Orthogonal Polynomials

- J. Baik
- MathematicsEncyclopedia of Special Functions: The Askey…
- 22 January 2007

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