Levin, David A. and Luczak, Malwina J. and Peres, Yuval
(2010)
*Glauber dynamics for the mean-field Ising model: cut-off, critical power law, and metastability.*
Probability Theory and Related Fields, 146 (1-2).
pp. 223-265.
ISSN 0178-8051

## Abstract

We study the Glauber dynamics for the Ising model on the complete graph, also known as the Curie–Weiss Model. For β < 1, we prove that the dynamics exhibits a cut-off: the distance to stationarity drops from near 1 to near 0 in a window of order n centered at [2(1 − β)]−1 n log n. For β = 1, we prove that the mixing time is of order n 3/2. For β > 1, we study metastability. In particular, we show that the Glauber dynamics restricted to states of non-negative magnetization has mixing time O(n log n).

Item Type: | Article |
---|---|

Official URL: | http://www.springer.com/mathematics/probability/jo... |

Additional Information: | © 2010 Springer |

Subjects: | Q Science > QA Mathematics |

Sets: | Departments > Mathematics |

Date Deposited: | 01 Dec 2010 12:18 |

Last Modified: | 23 Jan 2012 15:28 |

URI: | http://eprints.lse.ac.uk/id/eprint/29589 |

### Actions (login required)

View Item |