Glauber dynamics of continuous particle systems

Kondratiev, Yuri; Lytvynov, Eugene

doi:10.1016/j.anihpb.2004.05.002

Kondratiev, Yuri ; Lytvynov, Eugene

Annales de l'I.H.P. Probabilités et statistiques, Tome 41 (2005) no. 4, pp. 685-702

EuDML MR Zbl

DOI : 10.1016/j.anihpb.2004.05.002

@article{AIHPB_2005__41_4_685_0,
     author = {Kondratiev, Yuri and Lytvynov, Eugene},
     title = {Glauber dynamics of continuous particle systems},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     pages = {685--702},
     year = {2005},
     publisher = {Elsevier},
     volume = {41},
     number = {4},
     doi = {10.1016/j.anihpb.2004.05.002},
     mrnumber = {2144229},
     zbl = {1085.60074},
     language = {en},
     url = {https://www.numdam.org/articles/10.1016/j.anihpb.2004.05.002/}
}

TY  - JOUR
AU  - Kondratiev, Yuri
AU  - Lytvynov, Eugene
TI  - Glauber dynamics of continuous particle systems
JO  - Annales de l'I.H.P. Probabilités et statistiques
PY  - 2005
SP  - 685
EP  - 702
VL  - 41
IS  - 4
PB  - Elsevier
UR  - https://www.numdam.org/articles/10.1016/j.anihpb.2004.05.002/
DO  - 10.1016/j.anihpb.2004.05.002
LA  - en
ID  - AIHPB_2005__41_4_685_0
ER  -

%0 Journal Article
%A Kondratiev, Yuri
%A Lytvynov, Eugene
%T Glauber dynamics of continuous particle systems
%J Annales de l'I.H.P. Probabilités et statistiques
%D 2005
%P 685-702
%V 41
%N 4
%I Elsevier
%U https://www.numdam.org/articles/10.1016/j.anihpb.2004.05.002/
%R 10.1016/j.anihpb.2004.05.002
%G en
%F AIHPB_2005__41_4_685_0

Kondratiev, Yuri; Lytvynov, Eugene. Glauber dynamics of continuous particle systems. Annales de l'I.H.P. Probabilités et statistiques, Tome 41 (2005) no. 4, pp. 685-702. doi: 10.1016/j.anihpb.2004.05.002

Bibliographie
Cité par

[1] S. Alberverio, Yu.G. Kondratiev, M. Röckner, Analysis and geometry on configuration spaces, J. Funct. Anal. 154 (1998) 444-500. | Zbl | MR

[2] S. Alberverio, Yu.G. Kondratiev, M. Röckner, Analysis and geometry on configuration spaces. The Gibbsian case, J. Funct. Anal. 157 (1998) 242-291. | Zbl | MR

[3] S. Albeverio, M. Röckner, Dirichlet form methods for uniqueness of martigale problems and applications, in: Cranston M.C., Pinsky M.A. (Eds.), Stochastic Analysis, Proceedings of Symposia in Pure Mathematics, vol. 57, Amer. Math. Soc., 1995, pp. 513-528. | Zbl | MR

[4] Yu.M. Berezansky, Yu.G. Kondratiev, Spectral Methods in Infinite Dimensional Analysis, Kluwer Academic, Dordrecht, 1994. | Zbl

[5] Yu.M. Berezansky, Yu.G. Kondratiev, T. Kuna, E. Lytvynov, On a spectral representation for correlation measures in configuration space analysis, Methods Funct. Anal. Topol. 5 (4) (1999) 87-100. | Zbl | MR

[6] L. Bertini, N. Cancrini, F. Cesi, The spectral gap for a Glauber-type dynamics in a continuous gas, Ann. Inst. H. Poincaré Probab. Statist. 38 (2002) 91-108. | Zbl | MR | Numdam

[7] M. Fukushima, Dirichlet Forms and Symmetric Markov Processes, North-Holland, Amsterdam, 1980.

[8] R.A. Holley, D.W. Stroock, Nearest neighbor birth and death processes on the real line, Acta Math. 140 (1987) 103-154. | Zbl | MR

[9] O. Kallenberg, Random Measures, Academic Press, 1975. | Zbl | MR

[10] Yu.G. Kondratiev, Dirichlet operators and the smoothness of solutions of infinite-dimensional elliptic equations, Dokl. Akad. Nauk SSSR 282 (1985) 269-273, (in Russian). | Zbl | MR

[11] Yu.G. Kondratiev, T. Kuna, Harmonic analysis on configuration spaces I. General theory, Infin. Dimens. Anal. Quantum Probab. Relat. Top. 5 (2002) 201-233. | Zbl | MR

[12] T. Kuna, Studies in configuration space analysis and applications, PhD Thesis, Bonn University, 1999. | Zbl | MR

[13] T. Kuna, Properties of marked Gibbs measures in high temperature regime, Methods Funct. Anal. Topol. 7 (3) (2001) 33-53. | Zbl | MR

[14] Z.-M. Ma, M. Röckner, An Introduction to the Theory of (Non-Symmetric) Dirichlet Forms, Springer-Verlag, 1992. | Zbl

[15] Z.-M. Ma, M. Röckner, Construction of diffusions on configuration spaces, Osaka J. Math. 37 (2000) 273-314. | Zbl | MR

[16] X.X. Nguyen, H. Zessin, Integral and differentiable characterizations of the Gibbs process, Math. Nachr. 88 (1979) 105-115. | Zbl | MR

[17] C. Preston, Spatial birth-and-death processes, in: Proceedings of the 40th Session of the International Statistical Institute (Warsaw, 1975), vol. 2, Bull. Inst. Internat. Statist., vol. 46, 1975, pp. 371-391. | Zbl | MR

[18] M. Reed, B. Simon, Methods of Modern Mathematical Physics, vol. 2. Fourier Analysis, Self-Adjointness, Academic Press, 1972. | Zbl | MR

[19] M. Röckner, B. Schmuland, A support property for infinite-dimensional interacting diffusion processes, C. R. Acad. Sci. Paris, Sér. I 326 (1998) 359-364. | Zbl | MR

[20] D. Ruelle, Statistical Mechanics. Rigorous Results, Benjamins, 1969. | Zbl | MR

[21] D. Ruelle, Superstable interaction in classical statistical mechanics, Comm. Math. Phys. 18 (1970) 127-159. | Zbl | MR

[22] D. Surgailis, On multiple Poisson stochastic integrals and associated Markov semigroups, Probab. Math. Statist. 3 (1984) 217-239. | Zbl | MR

[23] D. Surgailis, On Poisson multiple stochastic integrals and associated equilibrium Markov processes, in: Theory and Application of Random Fields (Bangalore, 1982), Lecture Notes in Control and Inform. Sci., vol. 49, Springer, 1983, pp. 233-248. | Zbl | MR

[24] L. Wu, Estimate of spectral gap for continuous gas, preprint, 2003.

Cité par Sources :