Binary jumps in continuum. I. Equilibrium processes and their scaling limits

Finkelshtein DL, Kondratiev Y, Kutoviy OV, Lytvynov E (2011)
Journal of Mathematical Physics 52(6): 063304.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Finkelshtein, Dmitri L.; Kondratiev, YuriUniBi; Kutoviy, Oleksandr V.; Lytvynov, Eugene
Abstract / Bemerkung
Let Gamma denote the space of all locally finite subsets (configurations) in R(d). A stochastic dynamics of binary jumps in continuum is a Markov process on Gamma in which pairs of particles simultaneously hop over R(d). In this paper, we study an equilibrium dynamics of binary jumps for which a Poisson measure is a symmetrizing (and hence invariant) measure. The existence and uniqueness of the corresponding stochastic dynamics are shown. We next prove the main result of this paper: a big class of dynamics of binary jumps converge, in a diffusive scaling limit, to a dynamics of interacting Brownian particles. We also study another scaling limit, which leads us to a spatial birth-and-death process in continuum. A remarkable property of the limiting dynamics is that its generator possesses a spectral gap, a property which is hopeless to expect from the initial dynamics of binary jumps. (C) 2011 American Institute of Physics. [doi: 10.1063/1.3601118]
Erscheinungsjahr
2011
Zeitschriftentitel
Journal of Mathematical Physics
Band
52
Ausgabe
6
Art.-Nr.
063304
ISSN
0022-2488
Page URI
https://pub.uni-bielefeld.de/record/2307238

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Finkelshtein DL, Kondratiev Y, Kutoviy OV, Lytvynov E. Binary jumps in continuum. I. Equilibrium processes and their scaling limits. Journal of Mathematical Physics. 2011;52(6): 063304.
Finkelshtein, D. L., Kondratiev, Y., Kutoviy, O. V., & Lytvynov, E. (2011). Binary jumps in continuum. I. Equilibrium processes and their scaling limits. Journal of Mathematical Physics, 52(6), 063304. doi:10.1063/1.3601118
Finkelshtein, D. L., Kondratiev, Y., Kutoviy, O. V., and Lytvynov, E. (2011). Binary jumps in continuum. I. Equilibrium processes and their scaling limits. Journal of Mathematical Physics 52:063304.
Finkelshtein, D.L., et al., 2011. Binary jumps in continuum. I. Equilibrium processes and their scaling limits. Journal of Mathematical Physics, 52(6): 063304.
D.L. Finkelshtein, et al., “Binary jumps in continuum. I. Equilibrium processes and their scaling limits”, Journal of Mathematical Physics, vol. 52, 2011, : 063304.
Finkelshtein, D.L., Kondratiev, Y., Kutoviy, O.V., Lytvynov, E.: Binary jumps in continuum. I. Equilibrium processes and their scaling limits. Journal of Mathematical Physics. 52, : 063304 (2011).
Finkelshtein, Dmitri L., Kondratiev, Yuri, Kutoviy, Oleksandr V., and Lytvynov, Eugene. “Binary jumps in continuum. I. Equilibrium processes and their scaling limits”. Journal of Mathematical Physics 52.6 (2011): 063304.