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- Jinho Baik, Gérard Ben Arous, Sandrine Péché
- 2008

We compute the limiting distributions of the largest eigenvalue of a complex Gaussian sample covariance matrix when both the number of samples and the number of variables of each sample become large. When all but finitely many, say r, eigenvalues of the covariance matrix are equal to 1, the dependence of the limiting distribution of the largest eigenvalue… (More)

- JINHO BAIK, ERIC M. RAINS
- 2001

We compute the limiting distributions of the lengths of the longest monotone subse-quences of random (signed) involutions with or without conditions on the number of fixed points (and negated points) as the sizes of the involutions tend to infinity. The resulting distributions are, depending on the number of fixed points, (1) the Tracy-Widom distributions… (More)

- Jinho Baik, Eric M. Rains
- 2000

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 in [13]. Depending on the strength of the sources, the limiting distribution functions are either the Tracy-Widom functions of random matrix theory, or a new explicit function… (More)

We consider a spiked population model, proposed by Johnstone, whose population eigenvalues are all unit except for a few fixed eigenvalues. The question is to determine how the sample eigenvalues depend on the non-unit population ones when both sample size and population size become large. This paper completely determines the almost sure limits for a… (More)

- Jinho Baik, Eric M. Rains
- 1999

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 the distribution of the longest increasing subsequence of a random involution with constrained number of fixed points; new formulae for partial… (More)

- Jinho Baik, Eric M. Rains
- 1999

- Jinho Baik
- 2003

We present new and streamlined proofs of various formulae for products and ratios of characteristic polynomials of random Hermitian matrices that have appeared recently in the literature.

We compute the pointwise asymptotics of orthogonal polynomials with respect to a general class of pure point measures supported on finite sets as both the number of nodes of the measure and also the degree of the orthogonal polynomials become large. The class of orthogonal polynomials we consider includes as special cases the Krawtchouk and Hahn classical… (More)

In this paper, we obtain optimal uniform lower tail estimates for the probability distribution of the properly scaled length of the longest up/right path of the last passage site percolation model considered by Johansson in [12]. The estimates are used to prove a lower tail moderate deviation result for the model. The estimates also imply the convergence of… (More)

- Jinho Baik, Eri M. Rains
- 2001

We obtain an identity between Fredholm determinants of two kinds of operators, one acting on functions on the unit circle and the other acting on functions on a subset of the integers. This identity is a generalization of an identity between a Toeplitz determinant and a Fredholm determinant that has appeared in the random permutation context. Using this… (More)