About the L2 analyticity of markov operators on graphs

Joseph Feneuil

doi:10.1090/proc/13825

About the L₂ analyticity of markov operators on graphs

Joseph Feneuil

School of Mathematics

Research output: Contribution to journal › Article › peer-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 P^2k+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 language	English (US)
Pages (from-to)	1793-1805
Number of pages	13
Journal	Proceedings of the American Mathematical Society
Volume	146
Issue number	4
DOIs	https://doi.org/10.1090/proc/13825
State	Published - 2018

Bibliographical note

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

Publisher Copyright:
© 2017 American Mathematical Society.

Keywords

Discrete analyticity
Graphs
Lazy random walks
Markov chains

Publisher link

10.1090/proc/13825

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Cite this

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title = "About the L2 analyticity of markov operators on graphs",

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 {\textquoteleft}lazy{\textquoteright}, 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.",

keywords = "Discrete analyticity, Graphs, Lazy random walks, Markov chains",

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note = "Funding Information: The author was supported by the ANR project “Harmonic Analysis at its Boundaries”, ANR-12-BS01-0013-03. Publisher Copyright: {\textcopyright} 2017 American Mathematical Society.",

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