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A multi-dimensional Markov chain and the Meixner ensemble

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Arkiv för Matematik

Abstract

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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Authors and Affiliations

  1. Department of Mathematics, Royal Institute of Technology, SE-100 44, Stockholm, Sweden

    Kurt Johansson

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  1. Kurt Johansson
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Correspondence to Kurt Johansson.

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Johansson, K. A multi-dimensional Markov chain and the Meixner ensemble. Ark Mat 48, 79–95 (2010). https://doi.org/10.1007/s11512-008-0089-6

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  • DOI: https://doi.org/10.1007/s11512-008-0089-6

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