Arkiv för Matematik

A multi-dimensional Markov chain and the Meixner ensemble

Kurt Johansson

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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.

Article information

Source
Ark. Mat., Volume 48, Number 1 (2010), 79-95.

Dates
Received: 15 November 2007
First available in Project Euclid: 31 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.afm/1485907101

Digital Object Identifier
doi:10.1007/s11512-008-0089-6

Mathematical Reviews number (MathSciNet)
MR2594587

Zentralblatt MATH identifier
1197.60072

Rights
2008 © Institut Mittag-Leffler

Citation

Johansson, Kurt. A multi-dimensional Markov chain and the Meixner ensemble. Ark. Mat. 48 (2010), no. 1, 79--95. doi:10.1007/s11512-008-0089-6. https://projecteuclid.org/euclid.afm/1485907101


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