Levin, D, Luczak, Malwina and Peres, Y (2007) Glauber dynamics for the mean-field Ising model: cut-off, critical power law, and metastability. LSE-CDAM-2007-35. London school of economics and political science, London, UK.Full text not available from this repository.
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 n3/2. 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:||Monograph (Report)|
|Additional Information:||© 2007 London school of economics and political science|
|Library of Congress subject classification:||H Social Sciences > H Social Sciences (General)|
|Sets:||Departments > Mathematics
Research centres and groups > Computational, Discrete and Applicable Mathematics@LSE (CDAM)
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