## Abstract

Let Γ be a graph and P be a reversible random walk on Γ. From the L_{2} 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) |
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Pages (from-to) | 1793-1805 |

Number of pages | 13 |

Journal | Proceedings of the American Mathematical Society |

Volume | 146 |

Issue number | 4 |

DOIs | |

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

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