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Entropy decay and concentration for Strong Rayleigh measures via couplings

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Together with Justin Salez we establish universal modified log-Sobolev inequalities for reversible Markov chains on the boolean lattice {0,1}^n, under the only assumption that the invariant law pi satisfies a form of negative dependence known as the stochastic covering property. This condition is strictly weaker than the strong Rayleigh property, and is satisfied in particular by all determinantal measures, as well as by the uniform distribution over the set of bases of any balanced matroid and by the occupation measure of the exclusion process. This implies that one can rapidly sample from such distributions, a problem with numerous applications. In the special case where pi is k−homogeneous, our results imply the celebrated concentration inequality for Lipschitz functions due to Pemantle & Peres (2014).

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