Comparison inequality and two block estimate for inhomogeneous Bernoulli measures

Details Comparison inequality and two block estimate for inhomogeneous Bernoulli measures Comparison inequality and two block estimate for inhomogeneous Bernoulli measures

2003-03-11

arxiv.org/abs/math/0303132v3

Mathematics

Probability

Scientific paper

We consider inhomogeneous Bernoulli measures of the form $\prod_{x\in\Lambda} p_x$ where $p_x$ are prescribed and uniformly bounded above and below away from 0 and 1. A comparison inequality is proved between the Kawasaki and Bernoulli-Laplace Dirichlet forms. Together with a recent result of Caputo on the gap of the Bernoulli-Laplace model, this proves a spectral gap of the correct order L^{-2} on cubes of side length L for the Kawasaki dynamics. The two block estimate of hydrodynamic limits is also obtained.

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