On Gilles Pisier's approach to Gaussian concentration, isoperimetry, and Poincaré-type inequalities

DOI10.1214/24-ejp1104arXiv2311.03506OpenAlexW4392871525MaRDI QIDQ6126966

Sergey G. Bobkov, Bruno Volzone

Publication date: 10 April 2024

Published in: Electronic Journal of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2311.03506

zbMATH Keywords

Gaussian measuresSobolev-type inequalitiesCauchy measures

Mathematics Subject Classification ID

Inequalities; stochastic orderings (60E15) Operations with distributions and generalized functions (46F10)

Cites Work

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• Hardy-Poincaré inequalities and applications to nonlinear diffusions
• Inequalities for the gamma function
• Weighted Poincaré-type inequalities for Cauchy and other convex measures
• Analytic inequalities, isoperimetric inequalities and logarithmic Sobolev inequalities
• The Brunn-Minkowski inequality in Gauss space
• Convex measures on locally convex spaces
• Exponential integrability and transportation cost related to logarithmic Sobolev inequalities
• Isoperimetric and analytic inequalities for log-concave probability measures
• Isoperimetric problems for convex bodies and a localization lemma
• Rademacher type and Enflo type coincide
• Large deviations and isoperimetry over convex probability measures with heavy tails
• Sharp rates of decay of solutions to the nonlinear fast diffusion equation via functional inequalities
• Concentration and Gaussian Approximation for Randomized Sums
• Exponential integrability in Gauss space

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