Log concavity and concentration of Lipschitz functions on the Boolean hypercube

نویسندگان

چکیده

It is well-known that measures whose density the form e ? V where a uniformly convex potential on R n attain strong concentration properties. In search of notion log-concavity discrete hypercube, we consider { 1 , } multi-linear extension f satisfies log ? ? 2 ( x ) ? ? I for ? 0 which refer to as -semi-log-concave. We prove these satisfy nontrivial bound, namely, any Hamming Lipchitz test function ? Var ? [ ] ? C > . As corollary, bound exhibit so-called Rayleigh property. Namely, show such under external field (or exponential tilt), correlation between two coordinates non-positive, Hamming-Lipschitz functions admit concentration.

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ژورنال

عنوان ژورنال: Journal of Functional Analysis

سال: 2022

ISSN: ['0022-1236', '1096-0783']

DOI: https://doi.org/10.1016/j.jfa.2022.109392