Poincaré inequalities for inhomogeneous Bernoulli measures
نویسنده
چکیده
Recently there has been a lot of interest in the transport properties of particle systems in random media [AHL, BE, F, GP, KPW, K, MA, R, Se]. A simple model for which the hydrodynamic scaling limit can be obtained is the Kawasaki dynamics for random Bernoulli measures [Q], [QY]. Such systems have been used to model electron transport in doped crystals. The hydrodynamic limit is a nonlinear diffusion equation with a nontrivial density dependent diffusion coefficient given by a Green-Kubo formula. In fact for such a system even the existence of a diffusive scaling limit is nontrivial. The key input is a diffusive spectral gap, as well as a two block estimate [GPV]. In this article we give an elementary proof of the spectral gap and two block estimate for inhomogeneous Bernoulli measures with a bound depending on the bound on the external field. This work as well as [Q] and [QY] on the hydrodynamic limit, arose out of problems suggested to us by Herbert Spohn, whose contribution we gratefully acknowledge.
منابع مشابه
M ar 2 00 3 Poincare inequalities for inhomogeneous Bernoulli measures
x∈Λ px where px are prescribed and uniformly bounded above and below away from 0 and 1. Poincare inequalities are proved for the Glauber and Kawasaki dynamics, with constants of the same order as in the homogeneous case. 1. Inhomogeneous Bernoulli measures. Let hx ∈ [−K,K], x ∈ ZZ d be given and let px = ex 1 + ehx , x ∈ ZZ . For any Λ ⊂ ZZ d the inhomogeneous Bernoulli measure μΛ(η) on {0, 1} ...
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