Non-equilibrium stochastic dynamics in continuum: The free case

Kondratiev Y, Lytvynov E, Röckner M (2008)
CONDENSED MATTER PHYSICS 11(4): 701-721.

Konferenzbeitrag | Veröffentlicht | Englisch
 
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Abstract / Bemerkung
We study the problem of identification of a proper state-space for the stochastic dynamics of free particles in continuum, with their possible birth and death. In this dynamics, the motion of each separate particle is described by a fixed Markov process M on a Riemannian manifold X. The main problem arising here is a possible collapse of the system, in the sense that, though the initial configuration of particles is locally finite, there could exist a compact set in X such that, with probability one, infinitely many particles will arrive at this set at some time t > 0. We assume that X has infinite volume and, for each alpha >= 1, we consider the set Theta(alpha) of all infinite configurations in X for which the number of particles in a compact set is bounded by a constant times the alpha-th power of the volume of the set. We find quite general conditions on the process All which guarantee that the corresponding infinite particle process can start at each configuration from circle minus(alpha) will never leave circle minus(alpha) and has cadlag (or, even, continuous) sample paths in the vague topology. We consider the following examples of applications of our results: Brownian motion on the configuration space, free Glauber dynamics on the configuration space (or a birth-and-death process in X), and free Kawasaki dynamics on the configuration space. We also show that if X = R-d, then for a wide class of starting distributions, the (non-equilibrium) free Glauber dynamics is a scaling limit of (non-equilibrium) free Kawasaki dynamics.
Stichworte
process; Kawasaki dynamics; birth and death process; Brownian motion on the configuration space; independent infinite particle; Poisson measure; Glauber dynamics; continuous system
Erscheinungsjahr
2008
Band
11
Ausgabe
4
Seite(n)
701-721
ISSN
1607-324X
Page URI
https://pub.uni-bielefeld.de/record/1636273

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Kondratiev Y, Lytvynov E, Röckner M. Non-equilibrium stochastic dynamics in continuum: The free case. CONDENSED MATTER PHYSICS. 2008;11(4):701-721.
Kondratiev, Y., Lytvynov, E., & Röckner, M. (2008). Non-equilibrium stochastic dynamics in continuum: The free case. CONDENSED MATTER PHYSICS, 11(4), 701-721.
Kondratiev, Y., Lytvynov, E., and Röckner, M. (2008). Non-equilibrium stochastic dynamics in continuum: The free case. CONDENSED MATTER PHYSICS 11, 701-721.
Kondratiev, Y., Lytvynov, E., & Röckner, M., 2008. Non-equilibrium stochastic dynamics in continuum: The free case. CONDENSED MATTER PHYSICS, 11(4), p 701-721.
Y. Kondratiev, E. Lytvynov, and M. Röckner, “Non-equilibrium stochastic dynamics in continuum: The free case”, CONDENSED MATTER PHYSICS, vol. 11, 2008, pp. 701-721.
Kondratiev, Y., Lytvynov, E., Röckner, M.: Non-equilibrium stochastic dynamics in continuum: The free case. CONDENSED MATTER PHYSICS. 11, 701-721 (2008).
Kondratiev, Yuri, Lytvynov, Eugene, and Röckner, Michael. “Non-equilibrium stochastic dynamics in continuum: The free case”. CONDENSED MATTER PHYSICS 11.4 (2008): 701-721.