Sub-Gaussian estimates of heat kernels on infinite graphs

Sub-Gaussian estimates of heat kernels on infinite graphs

We prove that a two-sided sub-Gaussian estimate of the heat kernel on an infinite weighted graph takes place if and only if the volume growth of the graph is uniformly polynomial and the Green kernel admits a uniform polynomial decay.

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Duke mathematical journal 2001-09, Vol.109 (3), p.451-510
Hauptverfasser: Grigor'yan, Alexander, Telcs, Andras
Format: Artikel
Sprache:eng
Schlagworte:
35K05
58J35
60G50
60J35
60J45
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung:We prove that a two-sided sub-Gaussian estimate of the heat kernel on an infinite weighted graph takes place if and only if the volume growth of the graph is uniformly polynomial and the Green kernel admits a uniform polynomial decay.
ISSN:0012-7094
1547-7398
DOI:10.1215/S0012-7094-01-10932-0