On convergence of generators of equilibrium dynamics of hopping particles to generator of a birth-and-death process in continuum
We deal with the two following classes of equilibrium stochastic dynamics of infinite particle systems in continuum: hopping particles (also called Kawasaki dynamics), i.e., a dynamics where each particle randomly hops over the space, and birth-and-death process in continuum (or Glauber dynamics),...
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| Date: | 2008 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут фізики конденсованих систем НАН України
2008
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| Series: | Condensed Matter Physics |
| Online Access: | http://dspace.nbuv.gov.ua/handle/123456789/119137 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | On convergence of generators of equilibrium dynamics of hopping particles to generator of a birth-and-death process in continuum / E. Lytvynov, P.T. Polara // Condensed Matter Physics. — 2008. — Т. 11, № 2(54). — С. 223-236. — Бібліогр.: 24 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | We deal with the two following classes of equilibrium stochastic dynamics of infinite particle systems in continuum:
hopping particles (also called Kawasaki dynamics), i.e., a dynamics where each particle randomly hops
over the space, and birth-and-death process in continuum (or Glauber dynamics), i.e., a dynamics where there
is no motion of particles, but rather particles die, or are born at random. We prove that a wide class of Glauber
dynamics can be derived as a scaling limit of Kawasaki dynamics. More precisely, we prove the convergence
of respective generators on a set of cylinder functions, in the L²-norm with respect to the invariant measure
of the processes. The latter measure is supposed to be a Gibbs measure corresponding to a potential of pair
interaction, in the low activity–high temperature regime. Our result generalizes that of [Random. Oper. Stoch.
Equa., 2007, 15, 105], which was proved for a special Glauber (Kawasaki, respectively) dynamics. |
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