Isoperimetry between exponential and Gaussian
Franck Barthe (LSProba), Patrick Cattiaux (CMAP, MODAL'X), Cyril, Roberto (LAMA)
TL;DR
This paper investigates the isoperimetric properties of product probability measures with tails between exponential and Gaussian, highlighting cases where coordinate half-spaces serve as near-optimal solutions.
Contribution
It provides detailed analysis and examples of measures with intermediate tail behavior, identifying coordinate half-spaces as approximate solutions to the isoperimetric problem.
Findings
Coordinate half-spaces are approximate isoperimetric solutions.
Examples of measures with tails between exponential and Gaussian.
Detailed characterization of the isoperimetric profile for these measures.
Abstract
We study in details the isoperimetric profile of product probability measures with tails between the exponential and the Gaussian regime. In particular we exhibit many examples where coordinate half-spaces are approximate solutions of the isoperimetric problem.
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Taxonomy
TopicsRandom Matrices and Applications · Stochastic processes and financial applications · Geometry and complex manifolds