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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https://hal.archives-ouvertes.fr/hal-01766650
Contributor : Nathael Gozlan <>
Submitted on : Friday, April 13, 2018 - 6:33:06 PM
Last modification on : Friday, October 4, 2019 - 1:11:38 AM

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  • HAL Id : hal-01766650, version 1
  • ARXIV : 1804.06133

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Nathaël Gozlan, Ronan Herry. MULTIPLE SETS EXPONENTIAL CONCENTRATION AND HIGHER ORDER EIGENVALUES. 2018. ⟨hal-01766650⟩

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