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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, 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
- 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)

- 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
- 2001

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) as the sizes of the involutions tend to infinity. The resulting distributions are, depending on the number of fixed points, (1) the TracyWidom distributions for… (More)

- Jinho Baik, Eric M. Rains
- 1999

Selecting N random points in a unit square corresponds to selecting a random permutation. Placing symmetry restrictions on the points, we obtain special kinds of permutations : involutions, signed permutations and signed involutions. We are interested in the statistics of the length (in numbers of points) of the longest up/right path in each symmetry type… (More)

- Jinho Baik
- 2005

In a recent study of large non-null sample covariance matrices, a new sequence of functions generalizing the GUE Tracy-Widom distribution of random matrix theory was obtained. This paper derives Painlevé formulas of these functions and use them to prove that they are indeed distribution functions. Applications of these new distribution functions to last… (More)

- Jinho Baik
- 2003

denotes the average of f with respect to dPa ,N . Recently there has been considerable interest in the averages of products and ratios of the characteristic polynomials DN@m ,H#5P i51 N (m2xi(H)) of random matrices with respect to various ensembles. Such averages are used, in particular, in making predictions about the moments of the Riemann-zeta function… (More)

- Jinho Baik
- 2000

Lock step walker model is a one-dimensional integer lattice walker model in discrete time. Suppose that initially there are infinitely many walkers on the non-negative even integer sites. At each tick of time, each walker moves either to its left or to its right with equal probability. The only constraint is that no two walkers can occupy the same site at… (More)

- Jinho Baik
- 2001

Last three years have seen new developments in the theory of last passage percolation, which has variety applications to random permutations, random growth and random vicious walks. It turns out that a few class of models have determinant formulas for the probability distribution, which can be analyzed asymptotically. One of the tools for the asymptotic… (More)