About the L2 analyticity of markov operators on graphs

Joseph Feneuil

Research output: Contribution to journalArticlepeer-review

Abstract

Let Γ be a graph and P be a reversible random walk on Γ. From the L2 analyticity of the Markov operator P, we deduce that an iterate of odd exponent of P is ‘lazy’, that is, there exists an integer k such that the transition probability (for the random walk P2k+1) from a vertex x to itself is uniformly bounded from below. The proof does not require the doubling property on G but only a polynomial control of the volume.

Original languageEnglish (US)
Pages (from-to)1793-1805
Number of pages13
JournalProceedings of the American Mathematical Society
Volume146
Issue number4
DOIs
StatePublished - 2018

Bibliographical note

Funding Information:
The author was supported by the ANR project “Harmonic Analysis at its Boundaries”, ANR-12-BS01-0013-03.

Keywords

  • Discrete analyticity
  • Graphs
  • Lazy random walks
  • Markov chains

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