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. doi:10.1214/08-AIHP305

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Abstract

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
ISSN:	0246-0203
Official Date:	November 2009
Dates:	Date Event November 2009 Published
Volume:	Vol.45
Number:	No.4
Number of Pages:	20
Page Range:	pp. 1165-1184
DOI:	10.1214/08-AIHP305
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
Funder:	Science Foundation Ireland
Grant number:	SFI04/RP1/I512

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