One-particle subspace of the Glauber dynamics generator for continuous particle systems

Kondratiev Y, Minlos R, Zhizhina E (2004)
REVIEWS IN MATHEMATICAL PHYSICS 16(9): 1073-1114.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Kondratiev, YuriUniBi; Minlos, Robert; Zhizhina, Elena
Abstract / Bemerkung
We consider a Glauber-type stochastic dynamics of continuous particle systems in R-d. We construct a one-particle invariant subspace of the generator of this dynamics in the high temperature and low density regime. We prove that under some additional assumptions on the decay of the potential the restriction of the generator on the one-particle subspace is unitary equivalent to the operator of the multiplication by a bounded smooth realvalued function. As a consequence we estimate the spectral gap of the generator and find the second gap between the one-particle branch and the rest of the spectrum.
Stichworte
K-transform spectral analysis of the generator; Gibbs measures; equilibrium spatial birth and death processes
Erscheinungsjahr
2004
Zeitschriftentitel
REVIEWS IN MATHEMATICAL PHYSICS
Band
16
Ausgabe
9
Seite(n)
1073-1114
ISSN
0129-055X
Page URI
https://pub.uni-bielefeld.de/record/1605204

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Kondratiev Y, Minlos R, Zhizhina E. One-particle subspace of the Glauber dynamics generator for continuous particle systems. REVIEWS IN MATHEMATICAL PHYSICS. 2004;16(9):1073-1114.
Kondratiev, Y., Minlos, R., & Zhizhina, E. (2004). One-particle subspace of the Glauber dynamics generator for continuous particle systems. REVIEWS IN MATHEMATICAL PHYSICS, 16(9), 1073-1114. doi:10.1142/S0129055X04002217
Kondratiev, Y., Minlos, R., and Zhizhina, E. (2004). One-particle subspace of the Glauber dynamics generator for continuous particle systems. REVIEWS IN MATHEMATICAL PHYSICS 16, 1073-1114.
Kondratiev, Y., Minlos, R., & Zhizhina, E., 2004. One-particle subspace of the Glauber dynamics generator for continuous particle systems. REVIEWS IN MATHEMATICAL PHYSICS, 16(9), p 1073-1114.
Y. Kondratiev, R. Minlos, and E. Zhizhina, “One-particle subspace of the Glauber dynamics generator for continuous particle systems”, REVIEWS IN MATHEMATICAL PHYSICS, vol. 16, 2004, pp. 1073-1114.
Kondratiev, Y., Minlos, R., Zhizhina, E.: One-particle subspace of the Glauber dynamics generator for continuous particle systems. REVIEWS IN MATHEMATICAL PHYSICS. 16, 1073-1114 (2004).
Kondratiev, Yuri, Minlos, Robert, and Zhizhina, Elena. “One-particle subspace of the Glauber dynamics generator for continuous particle systems”. REVIEWS IN MATHEMATICAL PHYSICS 16.9 (2004): 1073-1114.