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- W2963794055 abstract "We study a class of logarithmic Sobolev inequalities with a general form of the energy functional. The class generalizes various examples of modified logarithmic Sobolev inequalities considered previously in the literature. Refining a method of Aida and Stroock for the classical logarithmic Sobolev inequality, we prove that if a measure on ℝn satisfies a modified logarithmic Sobolev inequality then it satisfies a family of Lp-Sobolev-type inequalities with non-Euclidean norms of gradients (and dimension-independent constants). The latter are shown to yield various concentration-type estimates for deviations of smooth (not necessarily Lipschitz) functions and measures of enlargements of sets corresponding to non-Euclidean norms. We also prove a two-level concentration result for functions of bounded Hessian and measures satisfying the classical logarithmic Sobolev inequality." @default.
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- W2963794055 date "2017-01-01" @default.
- W2963794055 modified "2023-09-27" @default.
- W2963794055 title "Moment estimates implied by modified log-Sobolev inequalities" @default.
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- W2963794055 doi "https://doi.org/10.1051/ps/2016030" @default.
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