数学物理学报(英文版) ›› 2009, Vol. 29 ›› Issue (5): 1461-1468.doi: 10.1016/S0252-9602(09)60118-1

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CONVEX CONCENTRATION INEQUALITIES FOR CONTINUOUS GAS AND STOCHASTIC DOMINATION

 马宇韬   

  1. School of Mathematical Sciences &|Laboratory of Mathematics and Complex Systems, Beijing Normal University, Beijing 100875, China
  • 收稿日期:2006-12-12 出版日期:2009-09-20 发布日期:2009-09-20
  • 基金资助:

    Supported by the NSFC (10721091)

CONVEX CONCENTRATION INEQUALITIES FOR CONTINUOUS GAS AND STOCHASTIC DOMINATION

 MA Yu Tao   

  1. School of Mathematical Sciences &|Laboratory of Mathematics and Complex Systems, Beijing Normal University, Beijing 100875, China
  • Received:2006-12-12 Online:2009-09-20 Published:2009-09-20
  • Supported by:

    Supported by the NSFC (10721091)

摘要:

In this article,  we consider the continuous gas in a bounded domain ∧of R+ or Rd described by a Gibbsian probability measure
μη associated with a pair interaction Φ, the inverse temperature β, the activity z>0, and the boundary condition η. Define F=∫f(s)ω∧(ds). Applying the generalized Ito's formula for forward-backward martingales (see Klein et al. [5]), we obtain convex concentration inequalities for F
with respect to the Gibbs measure μη. On the other hand, by FKG inequality on the Poisson space, we also give a new simple argument for the stochastic domination for the Gibbs measure.

关键词: continuous gas, Gibbs measure, convex concentration inequality, Itos formula, stochastic domination

Abstract:

In this article,  we consider the continuous gas in a bounded domain ∧of R+ or Rd described by a Gibbsian probability measure
μη associated with a pair interaction Φ, the inverse temperature β, the activity z>0, and the boundary condition η. Define F=∫f(s)ω∧(ds). Applying the generalized Ito's formula for forward-backward martingales (see Klein et al. [5]), we obtain convex concentration inequalities for F
with respect to the Gibbs measure μη. On the other hand, by FKG inequality on the Poisson space, we also give a new simple argument for the stochastic domination for the Gibbs measure.

Key words: continuous gas, Gibbs measure, convex concentration inequality, Itos formula, stochastic domination

中图分类号: 

  • 60E15