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arXiv · 1804.06133

Multiple sets exponential concentration and higher order eigenvalues

Nathaël Gozlan·Ronan Herry
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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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Nathaël Gozlan, Ronan Herry. 2018-04-17. Multiple sets exponential concentration and higher order eigenvalues. https://doi.org/10.1007/s11118-018-9743-1

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