# Modified log-Sobolev inequalities for strong-Rayleigh measures

@article{Hermon2019ModifiedLI, title={Modified log-Sobolev inequalities for strong-Rayleigh measures}, author={Jonathan Hermon and Justin Salez}, journal={arXiv: Probability}, year={2019} }

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 \emph{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 any product measure over the set of bases of a balanced matroid. In the special case where… CONTINUE READING

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