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Zap. Nauchn. Sem. POMI, 2012, Volume 403, Pages 81–94 (Mi znsl5249)  

Equilibrium Kawasaki dynamics and determinantal point processes

E. Lytvynova, G. Olshanskibcd

a Department of Mathematics, Swansea University, Swansea, UK
b Independent University of Moscow, Moscow, Russia
c Department of Mathematics, Higher School of Economics, Moscow, Russia
d Institute for Information Transmission Problems, Moscow, Russia

Abstract: 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 $\ell^2(\mathfrak X)$.

Key words and phrases: determinantal point process, gamma kernel, Gamma kernel measure, Kawasaki dynamics.

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English version:
Journal of Mathematical Sciences (New York), 2013, 190:3, 451–458

Bibliographic databases:

UDC: 519.217
Received: 13.06.2012
Language:

Citation: E. Lytvynov, G. Olshanski, “Equilibrium Kawasaki dynamics and determinantal point processes”, Representation theory, dynamical systems, combinatorial methods. Part XXI, Zap. Nauchn. Sem. POMI, 403, POMI, St. Petersburg, 2012, 81–94; J. Math. Sci. (N. Y.), 190:3 (2013), 451–458

Citation in format AMSBIB
\Bibitem{LytOls12}
\by E.~Lytvynov, G.~Olshanski
\paper Equilibrium Kawasaki dynamics and determinantal point processes
\inbook Representation theory, dynamical systems, combinatorial methods. Part~XXI
\serial Zap. Nauchn. Sem. POMI
\yr 2012
\vol 403
\pages 81--94
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl5249}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3029581}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2013
\vol 190
\issue 3
\pages 451--458
\crossref{https://doi.org/10.1007/s10958-013-1260-6}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84880632789}


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