Stability for the Brunn-Minkowski and Riesz rearrangement inequalities,\n with applications to Gaussian concentration and finite range non-local\n isoperimetry

2015/07/13 by Eric A. Carlen, Carlen, Eric A., Francesco Maggi +1
Mathematics · #FOS: Mathematics #FOS: Physical sciences #Mathematical Inequalities and Applications #Mathematical Physics (math-ph) #Numerical methods in inverse problems #Optimization and Control (math.OC) #Point processes and geometric inequalities #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.1507.03454

openalex publication_date 2015/07/13 · openalex created_date 2022/10/07 · openalex updated_date 2026/07/28

Abstract

We provide a simple, general argument to obtain improvements of\nconcentration-type inequalities starting from improvements of their\ncorresponding isoperimetric-type inequalities. We apply this argument to obtain\nrobust improvements of the Brunn-Minkowski inequality (for Minkowski sums\nbetween generic sets and convex sets) and of the Gaussian concentration\ninequality. The former inequality is then used to obtain a robust improvement\nof the Riesz rearrangement inequality under certain natural conditions. These\nconditions are compatible with the applications to a finite-range nonlocal\nisoperimetric problem arising in statistical mechanics.\n

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