A multi-dimensional Markov chain and the Meixner ensemble

Kurt Johansson Department of Mathematics, Royal Institute of Technology

TBD mathscidoc:1701.333162

Arkiv for Matematik, 48, (1), 79-95, 2007.11
We show that the transition probability of the Markov chain ($G$($i$,1),...,$G$($i$,$n$))_{$i$≥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.
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  title={A multi-dimensional Markov chain and the Meixner ensemble},
  author={Kurt Johansson},
  booktitle={Arkiv for Matematik},
Kurt Johansson. A multi-dimensional Markov chain and the Meixner ensemble. 2007. Vol. 48. In Arkiv for Matematik. pp.79-95. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203626426383971.
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