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 Pr\"ahofer and Spohn. 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 which has the special property that its mean is zero. Moreover, we obtain transition functions between pairs of the above distribution functions in suitably scaled limits. There are also similar results for a discrete totally asymmetric exclusion process.Comment: 15 pages, 1 figure, LaTe

Discrete Toeplitz/Hankel determinants and the width of non-intersecting processes

We show that the ratio of a discrete Toeplitz/Hankel determinant and its continuous counterpart equals a Freholm determinant involving continuous orthogonal polynomials. This identity is used to evaluate a triple asymptotic of some discrete Toeplitz/Hankel determinants which arise in studying non-intersecting processes. We show that the asymptotic fluctuations of the width of such processes are given by the GUE Tracy-Widom distribution. This result leads us to an identity between the GUE Tracy-Widom distribution and the maximum of the sum of two independent Airy processes minus a parabola. We provide an independent proof of this identity.Comment: 30 pages, 3 figure