### 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 |

Publisher | Association for Computing Machinery |

Pages | 1734-1740 |

Number of pages | 7 |

ISBN (Electronic) | 9781611975031 |

DOIs | |

State | Published - Jan 1 2018 |

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

### 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 |

### Fingerprint

### ASJC Scopus subject areas

- Software
- Mathematics(all)

### Cite this

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

**Comparing mixing times on sparse random graphs.** / Ben-Hamou, Anna; Lubetzky, Eyal; Peres, Yuval.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*29th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2018.*Association for Computing Machinery, pp. 1734-1740, 29th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2018, New Orleans, United States, 1/7/18. https://doi.org/10.1137/1.9781611975031.113

}

TY - GEN

T1 - Comparing mixing times on sparse random graphs

AU - Ben-Hamou, Anna

AU - Lubetzky, Eyal

AU - Peres, Yuval

PY - 2018/1/1

Y1 - 2018/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85045572944&partnerID=8YFLogxK

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U2 - 10.1137/1.9781611975031.113

DO - 10.1137/1.9781611975031.113

M3 - Conference contribution

AN - SCOPUS:85045572944

SP - 1734

EP - 1740

BT - 29th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2018

PB - Association for Computing Machinery

ER -