|
Zapiski Nauchnykh Seminarov POMI, 2012, Volume 403, Pages 81–94
(Mi znsl5249)
|
|
|
|
This article is cited in 1 scientific paper (total in 1 paper)
Equilibrium Kawasaki dynamics and determinantal point processes
E. Lytvynova, G. Olshanskibcd a Department of Mathematics, Swansea University, Swansea, UK
b Independent University of Moscow, Moscow, Russia
c Department of Mathematics, Higher School of Economics, Moscow, Russia
d Institute for Information Transmission Problems, Moscow, Russia
Abstract:
Let $\mu$ be a point process on a countable discrete space $\mathfrak X$. Under the assumption that $\mu$ is quasi-invariant with respect to any finitary permutation of $\mathfrak X$, we describe a general scheme for constructing an equilibrium Kawasaki dynamics for which $\mu$ is a symmetrizing (and hence invariant) measure. We also exhibit a two-parameter family of point processes $\mu$ possessing the needed quasi-invariance property. Each process of this family is determinantal, and its correlation kernel is the kernel of a projection operator in $\ell^2(\mathfrak X)$.
Key words and phrases:
determinantal point process, gamma kernel, Gamma kernel measure, Kawasaki dynamics.
Received: 13.06.2012
Citation:
E. Lytvynov, G. Olshanski, “Equilibrium Kawasaki dynamics and determinantal point processes”, Representation theory, dynamical systems, combinatorial methods. Part XXI, Zap. Nauchn. Sem. POMI, 403, POMI, St. Petersburg, 2012, 81–94; J. Math. Sci. (N. Y.), 190:3 (2013), 451–458
Linking options:
https://www.mathnet.ru/eng/znsl5249 https://www.mathnet.ru/eng/znsl/v403/p81
|
Statistics & downloads: |
Abstract page: | 275 | Full-text PDF : | 50 | References: | 46 |
|