منابع مشابه
Mixing time of near-critical random graphs
Let C1 be the largest component of the Erdős–Rényi random graph G(n,p). The mixing time of random walk on C1 in the strictly supercritical regime, p = c/n with fixed c > 1, was shown to have order log n by Fountoulakis and Reed, and independently by Benjamini, Kozma and Wormald. In the critical window, p = (1 + ε)/n where λ= εn is bounded, Nachmias and Peres proved that the mixing time on C1 is...
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Let C1 denote the largest connected component of the critical Erdős– Rényi random graph G(n, 1 n ). We show that, typically, the diameter of C1 is of order n1/3 and the mixing time of the lazy simple random walk on C1 is of order n. The latter answers a question of Benjamini, Kozma and Wormald. These results extend to clusters of size n2/3 of p-bond percolation on any d-regular n-vertex graph w...
متن کاملCritical Random Graphs: Diameter and Mixing Time Asaf Nachmias and Yuval Peres
Let C1 denote the largest connected component of the critical ErdősRényi random graph G(n, 1 n ). We show that, typically, the diameter of C1 is of order n and the mixing time of the lazy simple random walk on C1 is of order n. The latter answers a question of Benjamini, Kozma and Wormald [5]. These results extend to clusters of size n of p-bond percolation on any d-regular n-vertex graph where...
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Suppose that G is a finite, connected graph and X is a lazy random walk on G. The lamplighter chain X associated with X is the random walk on the wreath product G = Z2 oG, the graph whose vertices consist of pairs (f, x) where f is a labeling of the vertices of G by elements of Z2 and x is a vertex in G. There is an edge between (f, x) and (g, y) in G if and only if x is adjacent to y in G and ...
متن کاملSpatial Mixing of Coloring Random Graphs
We study the strong spatial mixing (decay of correlation) property of proper q-colorings of random graphG(n, d/n) with a fixed d. The strong spatial mixing of coloring and related models have been extensively studied on graphs with bounded maximum degree. However, for typical classes of graphs with bounded average degree, such as G(n, d/n), an easy counterexample shows that colorings do not exh...
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ژورنال
عنوان ژورنال: The Annals of Probability
سال: 2012
ISSN: 0091-1798
DOI: 10.1214/11-aop647