Equilibrium Kawasaki dynamics and determinantal point processes

Eugene Lytvynov; Grigori Olshanski

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arXiv · 1210.1362

Equilibrium Kawasaki dynamics and determinantal point processes

Eugene Lytvynov·Grigori Olshanski

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Abstract

Let "mu" be a point process on a countable discrete space "X". Under assumption that "mu" is quasi-invariant with respect to any finitary permutation of "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 the Hilbert space of square-summable functions on "X".

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BibTeX RIS

Eugene Lytvynov, Grigori Olshanski. 2012-10-04. Equilibrium Kawasaki dynamics and determinantal point processes. https://arxiv.org/abs/1210.1362

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