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 mailto [Université Paris Descartes > MAP5 > > Professeur des universités]
Herry, Ronan mailto [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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