A multi-dimensional Markov chain and the Meixner ensemble

Abstract

We show that the transition probability of the Markoc chain $(G(j,1),...,G(j,n){)}_{j\ge 1}$, where the $G(i,j{)}^{\prime }s$ are certain directed last-passage times, is given by a determinant of a special form. An analogous formula has recently been obtained by Warren in a Brownian motion model. Furthermore we demonstrate that this formula leads to the Meixner ensemble when we compute the distribution function for $G(m,n)$. We also obtain the Fredholm determinant representation of this distribution, where the kernel has a double contour integral representation.

14 pages

References in corpus (2)

• Current Distribution and random matrix ensembles for an integrable asymmetric fragmentation process
• Determinantal transition kernels for some interacting particles on the line

Cited by in corpus (1)

• Determinantal transition kernels for some interacting particles on the line