期刊名称：Latin American Journal of Probability and Mathematical Statistics
电子版ISSN：1980-0436
出版年度：2021
卷号：18
期号：1
页码：855
DOI：10.30757/ALEA.v18-31
出版社：Instituto Nacional De Matemática Pura E Aplicada
摘要：We consider a generic modified logarithmic Sobolev inequality (mLSI) of the form Entµ(e f ) ≤ ρ 2 Eµ e fΓ(f) 2 for some difference operator Γ, and show how it implies two-level concentration inequalities akin to the Hanson–Wright or Bernstein inequality. This can be applied to the continuous (e. g. the sphere or bounded perturbations of product measures) as well as discrete setting (the symmetric group, finite measures satisfying an approximate tensorization property, . . . ). Moreover, we use modified logarithmic Sobolev inequalities on the symmetric group Sn and for slices of the hypercube to prove Talagrand’s convex distance inequality, and provide concentration inequalities for locally Lipschitz functions on Sn. Some examples of known statistics are worked out, for which we obtain the correct order of fluctuations, which is consistent with central limit theorems.
