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Статья

Equilibrium Kawasaki dynamics and determinantal point process

Journal of Mathematical Sciences. 2013. Vol. 190. No. 3. P. 451-458.
Olshanski G., Lytvynov E.

Let μ be a point on a countable discrete space [InlineMediaObject not available: see fulltext.]. Under the assumption that μ is quasi-invariant with respect to any finitary permutation of [InlineMediaObject not available: see fulltext.], we describe a general scheme for constructing an equilibrium Kawasaki dynamics for which μ is a symmetrizing (and hence invariant) measure. We also exhibit a two-parameter family of point process μ possessing the needed quasi-invariance property. Each process of this family is determinantal, and its correlation kernel is the kernel of a projection in ℓ2 ([InlineMediaObject not available: see fulltext.]). Bibliography: 17 titles.