no. 4
Estimate of spectral gap for continuous gas
Annales de l'I.H.P. Probabilités et statistiques, Tome 40 (2004) no. 4, pp. 387-409. 
@article{AIHPB_2004__40_4_387_0,
     author = {Wu, Liming},
     title = {Estimate of spectral gap for continuous gas},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     pages = {387--409},
     publisher = {Elsevier},
     volume = {40},
     number = {4},
     year = {2004},
     doi = {10.1016/j.anihpb.2003.11.003},
     mrnumber = {2070332},
     zbl = {1042.60073},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1016/j.anihpb.2003.11.003/}
}
TY  - JOUR
AU  - Wu, Liming
TI  - Estimate of spectral gap for continuous gas
JO  - Annales de l'I.H.P. Probabilités et statistiques
PY  - 2004
SP  - 387
EP  - 409
VL  - 40
IS  - 4
PB  - Elsevier
UR  - http://archive.numdam.org/articles/10.1016/j.anihpb.2003.11.003/
DO  - 10.1016/j.anihpb.2003.11.003
LA  - en
ID  - AIHPB_2004__40_4_387_0
ER  - 
%0 Journal Article
%A Wu, Liming
%T Estimate of spectral gap for continuous gas
%J Annales de l'I.H.P. Probabilités et statistiques
%D 2004
%P 387-409
%V 40
%N 4
%I Elsevier
%U http://archive.numdam.org/articles/10.1016/j.anihpb.2003.11.003/
%R 10.1016/j.anihpb.2003.11.003
%G en
%F AIHPB_2004__40_4_387_0
Wu, Liming. Estimate of spectral gap for continuous gas. Annales de l'I.H.P. Probabilités et statistiques, Tome 40 (2004) no. 4, pp. 387-409. doi : 10.1016/j.anihpb.2003.11.003. http://archive.numdam.org/articles/10.1016/j.anihpb.2003.11.003/

[1] C Ané, M Ledoux, On logarithmic Sobolev inequalities for continuous random walks on graphs, Probab. Theory Related Fields 116 (2000) 573-602. | MR | Zbl

[2] T Bodineau, B Heffler, The log-Sobolev inequality for unbounded spin systems, J. Funct. Anal. 166 (1) (1999) 168-178. | MR | Zbl

[3] T Bodineau, B Heffler, Correlation, spectral gap and log-Sobolev inequalities for unbounded spin systems, in: Differential Equations and Math. Phys., Amer. Math. Soc, Providence, RI, 2000, pp. 51-66. | MR | Zbl

[4] L Bertini, N Cancrini, F Cesi, The spectral gap for a Glauber-type dynamics in a continuous gas, Ann. Inst. H. Poincaré PR 38 (1) (2002) 91-108. | Numdam | MR | Zbl

[5] F Cesi, Quasi-factorisation of entropy and log-Sobolev inequalities for Gibbs random fields, Probab. Theory Related Fields 120 (2001) 569-584. | MR | Zbl

[6] P Dai Pra, A.M Paganoni, G Posta, Entropy inequalities for unbounded spin systems, Ann. Probab. 30 (4) (2000) 1959-1976. | MR | Zbl

[7] A Holley, D.W Stroock, Nearest neighbor birth and death processes on the real line, Acta Mathematica 140 (1978) 103-154. | MR | Zbl

[8] O Kallenberg, Foundations of Modern Probability, Springer-Verlag, 1997. | MR | Zbl

[9] F Martinelli, Lectures on Glauber dynamics for discrete spin models, in: Ecole d'Eté de Saint-Flour (1997), Lect. Notes in Math., vol. 1717, Springer, 1999, pp. 93-191. | MR | Zbl

[10] M Ledoux, Logarithmic Sobolev inequalities for unbounded spin systems revisited, in: Séminaire de Probabilités, Lect. Notes Math., vol. 1755, Springer, 2001, pp. 167-194. | Numdam | MR | Zbl

[11] T.M Ligget, Interacting Particle Systems, Springer-Verlag, 1985. | Zbl

[12] S.L Lu, H.T Yau, Spectral gap and logarithmic Sobolev inequality for Kawasaki and Glauber dynamics, Comm. Math. Phys. 156 (1993) 399-433. | MR | Zbl

[13] Yu. Kondratiev, E. Lytvynov, Glauber dynamics of continuous particle systems, Preprint, 2003.

[14] Y.H Mao, Strong ergodicity for Markov processes by coupling method, J. Appl. Probab. 39 (4) (2002) 839-852. | MR | Zbl

[15] S Olla, C Tremoulet, Equilibrium fluctuations for interacting Ornstein-Uhlenbeck particles, Comm. Math. Phys. (2003). | Zbl

[16] J Picard, Formule de dualité sur l'espace de Poisson, Ann. Inst. H. Poincaré (Prob. Stat.) 32 (4) (1996) 509-548. | Numdam | MR | Zbl

[17] D Ruelle, Statistical Mechanics: Rigorous Results, Benjamin, 1969. | MR | Zbl

[18] D.W Stroock, B Zegarlinski, The equivalence between the logarithmic Sobolev inequality and the Dobrushin-Shlosman mixing condition, Comm. Math. Phys. 144 (1992) 303-323. | Zbl

[19] D.W Stroock, B Zegarlinski, The logarithmic Sobolev inequality for discrete spin systems on the lattice, Comm. Math. Phys. 149 (1992) 175-193. | MR | Zbl

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

[21] L Wu, A new modified logarithmic Sobolev inequality for Poisson point processes and several applications, Probab. Theory Related Fields 118 (2000) 427-438. | MR | Zbl

[22] L Wu, Uniqueness of Nelson's diffusions, Probab. Theory Related Fields 114 (1999) 549-585. | MR | Zbl

[23] N Yoshida, The equivalence of the logarithmic Sobolev inequality and a mixing condition for unbounded spin systems on the lattice, Ann. Inst. H. Poincaré (Prob. Stat.) 37 (2001) 223-243. | Numdam | MR | Zbl

Cité par Sources :