Stability of the Prekopa-Leindler inequality for log-concave functions

2020/07/30 by Károly J. Böröczky, Boroczky, Karoly J., Apratim De +1 · 5 citations
Mathematics · #26D15 #Advanced Banach Space Theory #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Inequalities and Applications #Point processes and geometric inequalities #Probability (math.PR)

paper · doi:10.48550/arxiv.2007.15304

openalex publication_date 2020/07/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Stability version of the Prekopa-Leindler inequality for log-concave functions on the n-dimensional Euclidean space is established.

Citations

• Remarks on the conjectured log-Brunn–Minkowski inequality
• Sampling from a log-concave distribution with Projected Langevin Monte\n Carlo

Cited by

• Quantitative stability of extremal quasi conformal mappings
• On the conjectured capillary Blaschke-Santaló inequality
• Sharp stability in hypercontractivity estimates and logarithmic Sobolev inequalities
• A parabolic PDE-based approach to Borell–Brascamp–Lieb inequality
• Regularized Moment Measures

Related

• Improved stability versions of the Prékopa-Leindler inequality
• A quantitative stability result for the Prékopa-Leindler inequality for arbitrary measurable functions
• Stability of some versions of the Prékopa-Leindler inequality
• Sharp Quantitative Stability for the Prékopa-Leindler and Borell-Brascamp-Lieb Inequalities
• A stochastic Prekopa-Leindler inequality for log-concave functions