Painleve formulas of the limiting distributions for non-null complex sample covariance matrices

Details Painleve formulas of the limiting distributions for non-null complex sample covariance matrices Painleve formulas of the limiting distributions for non-null complex sample covariance matrices

2005-04-29

arxiv.org/abs/math/0504606v2

Mathematics

Probability

24 pages, 1 Figure

Scientific paper

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 Painlev\'e formulas of these functions and use them to prove that they are indeed distribution functions. Applications of these new distribution functions to last passage percolation, queues in tandem and totally asymmetric simple exclusion process are also discussed. As a part of the proof, a representation of orthogonal polynomials on the unit circle in terms of an operator on a discrete set is presented.

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