Random conductance models with stable-like jumps: Heat kernel estimates and Harnack inequalities

Xin Chen, Takashi Kumagai, Jian Wang*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

Abstract

We establish two-sided heat kernel estimates for random conductance models with non-uniformly elliptic (possibly degenerate) stable-like jumps on graphs. These are long range counterparts of the well known two-sided Gaussian heat kernel estimates by M.T. Barlow for nearest neighbor (short range) random walks on the supercritical percolation cluster. Unlike the cases of nearest neighbor conductance models, we cannot use parabolic Harnack inequalities since even elliptic Harnack inequalities do not hold in the present setting. As an application, we establish the local limit theorem for the models.

Original languageEnglish
Article number108656
JournalJournal of Functional Analysis
Volume279
Issue number7
DOIs
Publication statusPublished - 2020 Oct 15
Externally publishedYes

Keywords

  • Conductance models with stable-like jumps
  • Dynkin-Hunt formula
  • Harnack inequality
  • Heat kernel estimate

ASJC Scopus subject areas

  • Analysis

Fingerprint

Dive into the research topics of 'Random conductance models with stable-like jumps: Heat kernel estimates and Harnack inequalities'. Together they form a unique fingerprint.

Cite this