### Abstract

It is natural to expect that nonbacktracking random walk will mix faster than simple random walks, but so far this has only been proved in regular graphs. To analyze typical irregular graphs, let G be a random graph on n vertices with minimum degree 3 and a degree distribution that has exponential tails. We determine the precise worst-case mixing time for simple random walk on G, and show that, with high probability, it exhibits cutof at time h^{-1} log n, where h is the asymptotic entropy for simple random walk on a Galton-Watson tree that approximates G locally. (Previously this was only known for typical starting points.) Furthermore, we show this asymptotic mixing time is strictly larger than the mixing time of nonbacktracking walk, via a delicate comparison of entropies on the Galton-Watson tree.

Original language | English (US) |
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Title of host publication | 29th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2018 |

Editors | Artur Czumaj |

Publisher | Association for Computing Machinery |

Pages | 1734-1740 |

Number of pages | 7 |

ISBN (Electronic) | 9781611975031 |

DOIs | |

State | Published - 2018 |

Event | 29th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2018 - New Orleans, United States Duration: Jan 7 2018 → Jan 10 2018 |

### Publication series

Name | Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms |
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### Other

Other | 29th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2018 |
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Country | United States |

City | New Orleans |

Period | 1/7/18 → 1/10/18 |

### ASJC Scopus subject areas

- Software
- Mathematics(all)

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## Cite this

*29th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2018*(pp. 1734-1740). (Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms). Association for Computing Machinery. https://doi.org/10.1137/1.9781611975031.113