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Comparison inequality and two block estimate for inhomogeneous Bernoulli measures

Jeremy Quastel
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Abstract

We consider inhomogeneous Bernoulli measures of the form $\prod_{x\inΛ} p_x$ 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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Jeremy Quastel. 2003-04-29. Comparison inequality and two block estimate for inhomogeneous Bernoulli measures. https://arxiv.org/abs/math/0303132

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