ERGODICITY FOR INFINITE PARTICLE SYSTEMS WITH LOCALLY CONSERVED QUANTITIES

被引：9

作者：

Inglis, J. ^{[1
]}

Neklyudov, M. ^{[2
]}

Zegarlinski, B. ^{[3
]}

机构：

[1] Univ London Imperial Coll Sci Technol & Med, Dept Math, London SW7 2AZ, England

[2] Univ York, Dept Math, Heslington, England

[3] Ctr Natl Rech Sci, Toulouse, France

来源：

INFINITE DIMENSIONAL ANALYSIS QUANTUM PROBABILITY AND RELATED TOPICS | 2012年 / 15卷 / 01期

基金：

英国工程与自然科学研究理事会;

关键词：

Hormander-type generators; locally conserved quantities; Liggett-Nash inequality; ergodicity; COERCIVE INEQUALITIES; HARMONIC-OSCILLATORS; EQUILIBRIUM; CONVERGENCE; THEOREM;

D O I：

10.1142/S0219025712500051

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We analyse degenerate infinite-dimensional sub-elliptic generators, and obtain estimates on the long-time behaviour of the corresponding Markov semigroups that describe a model of heat conduction. In particular, we establish ergodicity of the system for a family of invariant measures, and show that the optimal rate of convergence to equilibrium is polynomial. Consequently, there is no spectral gap, but a Liggett-Nash-type inequality is shown to hold.

引用

页数：28

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