Heat Kernel estimates and parabolic harnack inequalities on graphs and resistance forms

Takashi Kumagai*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

29 Citations (Scopus)

Abstract

We summarize recent work on heat kernel estimates and parabolic Harnack inequalities for graphs, where the time scale is the β-th power of the space scale for some β ≥ 2. We then discuss self-adjoint operators induced by resistance forms. Using a resistance metric, we give a simple condition for detailed heat kernel estimates and parabolic Harnack inequalities. As an application, we show that on trees a detailed two-sided heat kernel estimate is equivalent to some volume growth condition.

Original languageEnglish
Pages (from-to)793-818
Number of pages26
JournalPublications of the Research Institute for Mathematical Sciences
Volume40
Issue number3
DOIs
Publication statusPublished - 2004 Sep
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics(all)

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