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A multi-dimensional Markov chain and the Meixner ensemble
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0003-2943-7006
2010 (English)In: Arkiv för matematik, ISSN 0004-2080, E-ISSN 1871-2487, Vol. 48, no 1, 79-95 p.Article in journal (Refereed) Published
Abstract [en]

We show that the transition probability of the Markov chain (G(i,1),...,G(i,n)) (ia parts per thousand yen1), 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.

Place, publisher, year, edition, pages
2010. Vol. 48, no 1, 79-95 p.
Keyword [en]
simple exclusion process, random-matrix ensembles, growth
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-19228DOI: 10.1007/s11512-008-0089-6ISI: 000274685700005Scopus ID: 2-s2.0-77952883296OAI: oai:DiVA.org:kth-19228DiVA: diva2:337275
Note
QC 20110210Available from: 2010-08-05 Created: 2010-08-05 Last updated: 2017-12-12Bibliographically approved

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