Determinantal transition kernels for some interacting particles on the line

Dieker, A. B.; Warren, J.

Ann. Inst. H. Poincaré Probab. Statist., Tome 44 (2008) no. 2, p. 1162-1172 / Harvested from Project Euclid

Résumé

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.

Publié le : 2008-12-15
Classification: Interacting particle system, intertwining, Karlin–McGregor theorem, Markov transition kernel, Robinson–Schensted–Knuth correspondence, Schütz theorem, stochastic recursion, symmetric functions, 60J05, 60K35, 05E10, 05E05, 15A52

@article{1227287569,
     author = {Dieker, A. B. and Warren, J.},
     title = {Determinantal transition kernels for some interacting particles on the line},
     journal = {Ann. Inst. H. Poincar\'e Probab. Statist.},
     volume = {44},
     number = {2},
     year = {2008},
     pages = { 1162-1172},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1227287569}
}

Dieker, A. B.; Warren, J. Determinantal transition kernels for some interacting particles on the line. Ann. Inst. H. Poincaré Probab. Statist., Tome 44 (2008) no. 2, pp.  1162-1172. http://gdmltest.u-ga.fr/item/1227287569/