6533b821fe1ef96bd127b9dd

RESEARCH PRODUCT

Sharp dimension free quantitative estimates for the Gaussian isoperimetric inequality

Vesa JulinAlessio BrancoliniMarco Barchiesi

subject

Statistics and ProbabilityGaussianGaussian isoperimetric inequality01 natural sciencesPerimeterSet (abstract data type)symbols.namesakeMathematics - Analysis of PDEsDimension (vector space)quantitative isoperimetric inequalityFOS: MathematicsMathematics::Metric Geometry0101 mathematicsSymmetric differenceGaussian isoperimetric inequalityQuantitative estimatesMathematics010102 general mathematicsMathematical analysisProbability (math.PR)49Q20Gaussian measure010101 applied mathematicssymbolsHigh Energy Physics::Experiment60E15Statistics Probability and UncertaintyMathematics - ProbabilityAnalysis of PDEs (math.AP)

description

We provide a full quantitative version of the Gaussian isoperimetric inequality: the difference between the Gaussian perimeter of a given set and a half-space with the same mass controls the gap between the norms of the corresponding barycenters. In particular, it controls the Gaussian measure of the symmetric difference between the set and the half-space oriented so to have the barycenter in the same direction of the set. Our estimate is independent of the dimension, sharp on the decay rate with respect to the gap and with optimal dependence on the mass.

yearjournalcountryeditionlanguage
2017-03-01
https://dx.doi.org/10.48550/arxiv.1409.2106