Arkiv för Matematik
- Ark. Mat.
- Volume 48, Number 1 (2010), 79-95.
A multi-dimensional Markov chain and the Meixner ensemble
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.
Ark. Mat., Volume 48, Number 1 (2010), 79-95.
Received: 15 November 2007
First available in Project Euclid: 31 January 2017
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2008 © Institut Mittag-Leffler
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