Bendikov, Alexander and Pittet, Christophe and Sauer, Roman (2012) Spectral distribution and L-2-isoperimetric profile of Laplace operators on groups. MATHEMATISCHE ANNALEN, 354 (1). pp. 43-72. ISSN 0025-5831, 1432-1807
Full text not available from this repository. (Request a copy)Abstract
We give a formula relating the L (2)-isoperimetric profile to the spectral distribution of a Laplace operator on a finitely generated group I". We prove the asymptotic stability of the spectral distribution under changes of measures with finite second moment. As a consequence, we can apply techniques from geometric group theory to estimate the spectral distribution of the Laplace operator in terms of the growth and the Folner's function of the group. This leads to upper bounds on spectral distributions of some non-solvable amenable groups and to sharp estimates of the spectral distributions of some solvable groups with exponential growth.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | RANDOM-WALKS; LOWER BOUNDS; ISOPERIMETRY; |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 07 May 2020 12:03 |
| Last Modified: | 07 May 2020 12:03 |
| URI: | https://pred.uni-regensburg.de/id/eprint/18258 |
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