Determinantal transition kernels for some interacting particles on the line
Annales de l'I.H.P. Probabilités et statistiques, Volume 44 (2008) no. 6, pp. 1162-1172.

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.

Nous trouvons les noyaux de transition de quatre systèmes markoviens de particules en interaction sur une ligne, en prouvant que chacun de ces noyaux s'entrelace avec un noyau du type de Karlin-McGregor. Tous les noyaux résultants héritent de la structure de déterminant de la formule de Karlin-McGregor et ont une forme similaire à celle du noyau de Schütz pour le processus d'exclusion simple totalement asymétrique.

DOI: 10.1214/07-AIHP176
Classification: 60J05, 60K35, 05E10, 05E05, 15A52
Keywords: interacting particle system, intertwining, Karlin-McGregor theorem, Markov transition kernel, Robinson-Schensted-Knuth correspondence, Schütz theorem, stochastic recursion, symmetric functions
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     title = {Determinantal transition kernels for some interacting particles on the line},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     pages = {1162--1172},
     publisher = {Gauthier-Villars},
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Dieker, A. B.; Warren, J. Determinantal transition kernels for some interacting particles on the line. Annales de l'I.H.P. Probabilités et statistiques, Volume 44 (2008) no. 6, pp. 1162-1172. doi : 10.1214/07-AIHP176. http://www.numdam.org/articles/10.1214/07-AIHP176/

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