The spectral gap for a Glauber-type dynamics in a continuous gas

被引:50
作者
Bertini, L
Cancrini, N
Cesi, F
机构
[1] Univ Roma La Sapienza, Dipartimento Matemat, I-00185 Rome, Italy
[2] Univ Aquila, Dipartimento Energet, I-67100 Laquila, Italy
[3] Univ Roma La Sapienza, Dipartimento Fis, I-00185 Rome, Italy
[4] INFM, Unita Roma La Sapienza, Rome, Italy
来源
ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES | 2002年 / 38卷 / 01期
关键词
spectral gap; Gibbs measures; continuous systems; birth and death processes;
D O I
10.1016/S0246-0203(01)01085-8
中图分类号
O21 [概率论与数理统计]; C8 [统计学];
学科分类号
020208 ; 070103 ; 0714 ;
摘要
We consider a continuous gas in a d-dimensional rectangular box with a finite range, positive pair potential, and we construct a Markov process in which particles appear and disappear with appropriate rates so that the process is reversible w.r.t. the Gibbs measure. If the thermodynamical paramenters are such that the Gibbs specification satisfies a certain mixing condition, then the spectral gap of the generator is strictly positive uniformly in the volume and boundary condition. The required mixing condition holds if, for instance, there is a convergent cluster expansion. (C) 2002 Editions scientifiques et medicales Elsevier SAS.
引用
收藏
页码:91 / 108
页数:18
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