Determinantal transition kernels for some interacting particles on the line

A. B. Dieker; J. Warren

Annales de l'I.H.P. Probabilités et statistiques (2008)

  • Volume: 44, Issue: 6, page 1162-1172
  • ISSN: 0246-0203

Abstract

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We find the transition kernels for four markovian interacting particle systems on the line, by proving that each of these kernels is intertwined with a Karlin–McGregor-type kernel. The resulting kernels all inherit the determinantal structure from the Karlin–McGregor formula, and have a similar form to Schütz’s kernel for the totally asymmetric simple exclusion process.

How to cite

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Dieker, A. B., and Warren, J.. "Determinantal transition kernels for some interacting particles on the line." Annales de l'I.H.P. Probabilités et statistiques 44.6 (2008): 1162-1172. <http://eudml.org/doc/78007>.

@article{Dieker2008,
abstract = {We find the transition kernels for four markovian interacting particle systems on the line, by proving that each of these kernels is intertwined with a Karlin–McGregor-type kernel. The resulting kernels all inherit the determinantal structure from the Karlin–McGregor formula, and have a similar form to Schütz’s kernel for the totally asymmetric simple exclusion process.},
author = {Dieker, A. B., Warren, J.},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {interacting particle system; intertwining; Karlin–McGregor theorem; Markov transition kernel; Robinson–Schensted–Knuth correspondence; Schütz theorem; stochastic recursion; symmetric functions; Karlin-McGregor theorem; Robinson-Schensted-Knuth correspondence},
language = {eng},
number = {6},
pages = {1162-1172},
publisher = {Gauthier-Villars},
title = {Determinantal transition kernels for some interacting particles on the line},
url = {http://eudml.org/doc/78007},
volume = {44},
year = {2008},
}

TY - JOUR
AU - Dieker, A. B.
AU - Warren, J.
TI - Determinantal transition kernels for some interacting particles on the line
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2008
PB - Gauthier-Villars
VL - 44
IS - 6
SP - 1162
EP - 1172
AB - We find the transition kernels for four markovian interacting particle systems on the line, by proving that each of these kernels is intertwined with a Karlin–McGregor-type kernel. The resulting kernels all inherit the determinantal structure from the Karlin–McGregor formula, and have a similar form to Schütz’s kernel for the totally asymmetric simple exclusion process.
LA - eng
KW - interacting particle system; intertwining; Karlin–McGregor theorem; Markov transition kernel; Robinson–Schensted–Knuth correspondence; Schütz theorem; stochastic recursion; symmetric functions; Karlin-McGregor theorem; Robinson-Schensted-Knuth correspondence
UR - http://eudml.org/doc/78007
ER -

References

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