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Glauber dynamics for the mean-field Ising model: cut-off, critical power law, and metastability |
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| Authors: | David A Levin Malwina J Luczak Yuval Peres |
| Institution: | 1. Department of Mathematics, University of Oregon, Eugene, OR, 97403-1222, USA 2. Department of Mathematics, London School of Economics, Houghton Street, London, WC2A 2AE, UK 3. Microsoft Research, Redmond, WA, USA 4. University of Washington, Seattle, WA, USA 5. University of California, Berkeley, CA, USA |
| 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). |
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