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Journal Articles Potential Analysis Year : 2020

MULTIPLE SETS EXPONENTIAL CONCENTRATION AND HIGHER ORDER EIGENVALUES

Abstract

On a generic metric measured space, we introduce a notion of improved concentration of measure that takes into account the parallel enlargement of k distinct sets. We show that the k-th eigenvalues of the metric Laplacian gives exponential improved concentration with k sets. On compact Riemannian manifolds, this allows us to recover estimates on the eigenvalues of the Laplace-Beltrami operator in the spirit of an inequality of Chung, Grigory'an and Yau [11].
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Dates and versions

hal-01766650 , version 1 (13-04-2018)

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Nathaël Gozlan, Ronan Herry. MULTIPLE SETS EXPONENTIAL CONCENTRATION AND HIGHER ORDER EIGENVALUES. Potential Analysis, 2020, 52 (2), pp.203-221. ⟨10.1007/s11118-018-9743-1⟩. ⟨hal-01766650⟩
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