Equilibrium Kawasaki dynamics and determinantal point processes

2012/10/04 by Eugene Lytvynov, Lytvynov, Eugene, Grigori Olshanski +1
Mathematics · #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #Random Matrices and Applications

paper · pdf · doi:10.48550/arxiv.1210.1362

openalex publication_date 2012/10/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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