Glauber dynamics for the mean-field Ising model: cut-off, critical power law, and metastability
| dc.creator | Levin, David A. | |
| dc.creator | Luczak, Malwina J. | |
| dc.creator | Peres, Yuval | |
| dc.date | 2007-12-05 | |
| dc.date | 2007-12-10 | |
| dc.date.accessioned | 2026-07-07T08:47:52Z | |
| dc.date.available | 2026-07-07T08:47:52Z | |
| dc.description | We study the Glauber dynamics for the Ising model on the complete graph, also known as the Curie-Weiss Model. For beta < 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-beta)]^{-1} n log n. For beta = 1, we prove that the mixing time is of order n^{3/2}. For beta > 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). | |
| dc.description | 40 pages | |
| dc.identifier | https://arxiv.org/abs/0712.0790 | |
| dc.identifier | http://arxiv.org/abs/0712.0790 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/143752 | |
| dc.subject | Probability | |
| dc.subject | 60J10, 60K35, 82C20 | |
| dc.title | Glauber dynamics for the mean-field Ising model: cut-off, critical power law, and metastability | |
| dc.type | text |