Geodesic
Equilibrium Kawasaki dynamics and determinantal point processes
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXI, Tome 403 (2012), pp. 81-94 Cet article a éte moissonné depuis la source Math-Net.Ru

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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 $\ell^2(\mathfrak X)$. 
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E. Lytvynov; G. Olshanski. Equilibrium Kawasaki dynamics and determinantal point processes. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXI, Tome 403 (2012), pp. 81-94. http://geodesic.mathdoc.fr/item/ZNSL_2012_403_a4/

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