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5 papers · 2 filters
Glauber dynamics for the mean-field Ising model: cut-off, critical power law, and metastability
David A. Levin, Malwina J. Luczak, Yuval Peres
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 dista…
Boundary proximity of SLE
Oded Schramm, Wang Zhou
This paper examines how close the chordal $\SLE_κ$ curve gets to the real line asymptotically far away from its starting point. In particular, when , it is shown that if…
Mean-field conditions for percolation on finite graphs
Asaf Nachmias
Let G_n be a sequence of finite transitive graphs with vertex degree d=d(n) and |G_n|=n. Denote by p^t(v,v) the return probability after t steps of the non-backtracking random walk…
Card shuffling and diophantine approximation
Omer Angel, Yuval Peres, David B. Wilson
The ``overlapping-cycles shuffle'' mixes a deck of cards by moving either the th card or the th card to the top of the deck, with probability half each. We determine…
Critical random graphs: Diameter and mixing time
Asaf Nachmias, Yuval Peres
Let denote the largest connected component of the critical Erdős--Rényi random graph . We show that, typically, the diameter of …