Regularization under diffusion and anticoncentration of the information content

DOI10.1215/00127094-2017-0048zbMath1388.60058arXiv1410.3887OpenAlexW2764184559MaRDI QIDQ1750377

James R. Lee, Ronen Eldan

Publication date: 18 May 2018

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1410.3887

zbMATH Keywords

regularizationhypercontractivityOrnstein-Uhlenbeck semigroupGaussian space

Mathematics Subject Classification ID

Gaussian processes (60G15) Inequalities; stochastic orderings (60E15) Geometric probability and stochastic geometry (60D05) Applications of stochastic analysis (to PDEs, etc.) (60H30) Diffusion processes (60J60) Heat and other parabolic equation methods for PDEs on manifolds (58J35)

Related Items (9)

Regularization in \(L_1\) for the Ornstein-Uhlenbeck semigroup ⋮ Stability of hypercontractivity, the logarithmic Sobolev inequality, and Talagrand's cost inequality ⋮ Log-Hessian and deviation bounds for Markov semi-groups, and regularization effect in \(\mathbb{L}^1 \) ⋮ A Dimension-Free Reverse Logarithmic Sobolev Inequality for Low-Complexity Functions in Gaussian Space ⋮ The CLT in high dimensions: quantitative bounds via martingale embedding ⋮ Dimension-free log-Sobolev inequalities for mixture distributions ⋮ Ornstein–Uhlenbeck operators and semigroups ⋮ Stability of Talagrand's Gaussian transport-entropy inequality via the Föllmer process ⋮ Stability of the Shannon-Stam inequality via the Föllmer process

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