Bendikov, Alexander ; Pittet, Christophe ; Sauer, Roman
Alternative Links zum Volltext:DOIVerlag
| Dokumentenart: | Artikel |
|---|
| Titel eines Journals oder einer Zeitschrift: | Mathematische Annalen |
|---|
| Verlag: | SPRINGER HEIDELBERG |
|---|
| Ort der Veröffentlichung: | HEIDELBERG |
|---|
| Band: | 354 |
|---|
| Nummer des Zeitschriftenheftes oder des Kapitels: | 1 |
|---|
| Seitenbereich: | S. 43-72 |
|---|
| Datum: | 2012 |
|---|
| Institutionen: | Mathematik |
|---|
| Identifikationsnummer: | | Wert | Typ |
|---|
| 10.1007/s00208-011-0724-6 | DOI |
|
|---|
| Stichwörter / Keywords: | RANDOM-WALKS; LOWER BOUNDS; ISOPERIMETRY; |
|---|
| Dewey-Dezimal-Klassifikation: | 500 Naturwissenschaften und Mathematik > 510 Mathematik |
|---|
| Status: | Veröffentlicht |
|---|
| Begutachtet: | Ja, diese Version wurde begutachtet |
|---|
| An der Universität Regensburg entstanden: | Ja |
|---|
| Dokumenten-ID: | 63443 |
|---|
Zusammenfassung
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 ...
Zusammenfassung
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.
Altmetric