Multiple sets exponential concentration and higher order eigenvalues
Probability
2019-09-30 v1 Functional Analysis
Spectral Theory
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].
Cite
@article{arxiv.1804.06133,
title = {Multiple sets exponential concentration and higher order eigenvalues},
author = {Nathaël Gozlan and Ronan Herry},
journal= {arXiv preprint arXiv:1804.06133},
year = {2019}
}