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A multi-dimensional Markov chain and the Meixner ensemble | | Kurt Johansson
; | | Date: |
1 Jul 2007 | | Abstract: | We show that the transition probability of the Markoc chain
$(G(j,1),...,G(j,n))_{jge 1}$, where the $G(i,j)’s$ 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. | | Source: | arXiv, arxiv.0707.0098 | | Services: | Forum | Review | PDF | Favorites | |
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