Modified log-Sobolev inequalities for strong-Rayleigh measures
Hermon, Jonathan; Salez, Justin (2023), Modified log-Sobolev inequalities for strong-Rayleigh measures, Annals of Applied Probability, 33, 2, p. 1301-1314. 10.1214/22-AAP1847
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Type
Article accepté pour publication ou publiéDate
2023Journal name
Annals of Applied ProbabilityVolume
33Number
2Publisher
Institute of Mathematical Statistics
Published in
Paris
Pages
1301-1314
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Show full item recordAuthor(s)
Hermon, JonathanSalez, Justin
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)
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 π 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 any product measure over the set of bases of a balanced matroid. In the special case where π is k−homogeneous, our results imply the celebrated concentration inequality for Lipschitz functions due to Pemantle & Peres (2014). As another application, we deduce that the natural Monte-Carlo Markov Chain used to sample from π has mixing time at most knloglog1π(x) when initialized in state x. To the best of our knowledge, this is the first work relating negative dependence and modified log-Sobolev inequalities.Subjects / Keywords
Modified log-Sobolev inequalities; Negative dependence; stochastic coveringRelated items
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