Interlaced processes on the circle
Metcalfe, Anthony P., O'Connell, Neil and Warren, Jon. (2009) Interlaced processes on the circle. Annales de l’Institut Henri Poincaré - Probabilites et Statistiques, Vol.45 (No.4). pp. 1165-1184. ISSN 0246-0203Full text not available from this repository.
Official URL: http://dx.doi.org/10.1214/08-AIHP305
When two Markov operators commute, it suggests that we can couple two copies of one of the corresponding processes. We explicitly construct a number of couplings of this type for a commuting family of Markov processes on the set of conjugacy classes of the unitary group, using a dynamical rule inspired by the RSK algorithm. Our motivation for doing this is to develop a parallel programme, on the circle, to some recently discovered connections in random matrix theory between reflected and conditioned systems of particles on the line. One of the Markov chains we consider gives rise to a family of Gibbs measures on "bead configurations" on the infinite cylinder. We show that these measures have determinantal structure and compute the corresponding space-time correlation kernel.
|Item Type:||Journal Article|
|Subjects:||Q Science > QA Mathematics|
|Divisions:||Faculty of Science > Mathematics
Faculty of Science > Statistics
|Journal or Publication Title:||Annales de l’Institut Henri Poincaré - Probabilites et Statistiques|
|Publisher:||Institute of Mathematical Statistics|
|Number of Pages:||20|
|Page Range:||pp. 1165-1184|
|Access rights to Published version:||Restricted or Subscription Access|
|Funder:||Science Foundation Ireland|
Actions (login required)