| Reference : Multiple Sets Exponential Concentration and Higher Order Eigenvalues |
| Scientific journals : Article | |||
| Physical, chemical, mathematical & earth Sciences : Mathematics | |||
| http://hdl.handle.net/10993/37423 | |||
| Multiple Sets Exponential Concentration and Higher Order Eigenvalues | |
| English | |
Gozlan, Nathael  [Université Paris Descartes > MAP5 > > Professeur des universités] | |
| Herry, Ronan [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >] | |
| In press | |
| Potential Analysis | |
| Kluwer Academic Publishers | |
| Yes (verified by ORBilu) | |
| International | |
| 0926-2601 | |
| 1572-929X | |
| Amsterdam | |
| Netherlands | |
| [en] Concentration of measure phenomenon ; Eigenvalues of the Laplacian ; Poincaré inequality | |
| [en] 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, Grigor’yan & Yau, Upper bounds for eigenvalues of the discrete and continuous Laplace operators. Adv. Math. 117(2), 165–178 (1996). | |
| Researchers ; Professionals ; Students | |
| http://hdl.handle.net/10993/37423 | |
| 10.1007/s11118-018-9743-1 |
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