A Note on the Spectral Gap for Log-Concave Probability Measures on Convex Bodies
Copyright policy )A Note on the Spectral Gap for Log-Concave Probability Measures on Convex Bodies
Abstract In this paper, we provide explicit lower bounds with respect to some quantities of interest (parameters of the underlying distribution, dimension, geometrical characteristics of the domain, position of the origin, etc.) on the spectral gap of log-concave probability measures on convex bodies. Our results are illustrated by some classical and less classical examples.
[MATH.MATH-PR] Mathematics [math]/Probability [math.PR], Neumann eigenvalues, 37A30, 58J50 Spectral gap Neumann eigenvalues Poincaré type inequalities Log-concave probability measure, [MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA], Poincaré type inequalities, 510, 58J50 Spectral gap, Convex body, spectral gap, FOS: Mathematics, Probabilistic measure theory, convex bodies, 47D07, log-concavity, Probability (math.PR), [MATH.MATH-FA] Mathematics [math]/Functional Analysis [math.FA], Log-concave probability measure, Functional Analysis (math.FA), [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], Mathematics - Functional Analysis, probability measures, 39B62, Geometric probability and stochastic geometry, 2010 Mathematics Subject Classification. 60J60, Mathematics - Probability
[MATH.MATH-PR] Mathematics [math]/Probability [math.PR], Neumann eigenvalues, 37A30, 58J50 Spectral gap Neumann eigenvalues Poincaré type inequalities Log-concave probability measure, [MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA], Poincaré type inequalities, 510, 58J50 Spectral gap, Convex body, spectral gap, FOS: Mathematics, Probabilistic measure theory, convex bodies, 47D07, log-concavity, Probability (math.PR), [MATH.MATH-FA] Mathematics [math]/Functional Analysis [math.FA], Log-concave probability measure, Functional Analysis (math.FA), [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], Mathematics - Functional Analysis, probability measures, 39B62, Geometric probability and stochastic geometry, 2010 Mathematics Subject Classification. 60J60, Mathematics - Probability
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