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### Equilibrium Kawasaki dynamics and determinantal point process / E. Lytvynov, G. Olshanski, Eugene Lytvynov

Journal of Mathematical Sciences, Volume: 190, Issue: 3, Pages: 451 - 458

Swansea University Author:

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DOI (Published version): 10.1007/s10958-013-1260-6

Abstract

Let $\mu$ be a point process on a countable discrete space$\mathfrak X$. Under assumption that $\mu$ is quasi-invariant with respect toany finitary permutation of $\mathfrak X$, we describe a general scheme forconstructing an equilibrium Kawasaki dynamics for which $\mu$ is asymmetrizing (and hence...

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Published in: Journal of Mathematical Sciences 2013 http://link.springer.com/article/10.1007/s10958-013-1260-6 https://cronfa.swan.ac.uk/Record/cronfa19098 No Tags, Be the first to tag this record!
Abstract: Let $\mu$ be a point process on a countable discrete space$\mathfrak X$. Under assumption that $\mu$ is quasi-invariant with respect toany finitary permutation of $\mathfrak X$, we describe a general scheme forconstructing an equilibrium Kawasaki dynamics for which $\mu$ is asymmetrizing (and hence invariant) measure. We also exhibit a two-parameterfamily of point processes $\mu$ possessing the needed quasi-invarianceproperty. Each process of this family is determinantal, and its correlationkernel is the kernel of a projection operator in $\ell^2(\mathfrak X)$. College of Science 3 451 458