About the $L^2$ analyticity of Markov operators on graphs
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- by Joseph Feneuil PDF
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Abstract:
Let $\Gamma$ be a graph and $P$ be a reversible random walk on $\Gamma$. From the $L^2$ analyticity of the Markov operator $P$, we deduce that an iterate of odd exponent of $P$ is âlazyâ, 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 $\Gamma$ but only a polynomial control of the volume.References
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Additional Information
- Joseph Feneuil
- Affiliation: School of Mathematics, University of Minnesota, 127 Vincent Hall, 206 Church Street SE, Minneapolis, Minnesota 55455
- MR Author ID: 1119999
- Email: jfeneuil@umn.edu
- Received by editor(s): September 15, 2015
- Received by editor(s) in revised form: July 12, 2016, August 24, 2016, and May 17, 2017
- Published electronically: November 7, 2017
- Additional Notes: The author was supported by the ANR project âHarmonic Analysis at its Boundariesâ, ANR-12-BS01-0013-03.
- Communicated by: Mark M. Meerschaert
- © Copyright 2017 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 146 (2018), 1793-1805
- MSC (2010): Primary 60J10; Secondary 35P05, 47D07
- DOI: https://doi.org/10.1090/proc/13825
- MathSciNet review: 3754361