Invariance principle for the random conductance model with unbounded conductances
نویسندگان
چکیده
منابع مشابه
Invariance principle for the Random Conductance Model
We study a continuous time random walk X in an environment of i.i.d. random conductances μe ∈ [0,∞) in Zd. We assume that P(μe > 0) > pc, so that the bonds with strictly positive conductances percolate, but make no other assumptions on the law of the μe. We prove a quenched invariance principle for X, and obtain Green’s functions bounds and an elliptic Harnack inequality.
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We consider a random walk on a random graph (V,E), where V is the set of open sites under i.i.d. Bernoulli site percolation on the d-dimensional integer set Z with d ≥ 2, and the transition probabilities of the walk are generated by i.i.d. random conductances (positive numbers) assigned to the edges in E. This random walk in random environments has long range jumps and is reversible. We prove t...
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We consider a stationary and ergodic random field {ω(e) : e ∈ Ed} that is parameterized by the edge set of the Euclidean lattice Z, d ≥ 2. The random variable ω(e), taking values in [0,∞) and satisfying certain moment bounds, is thought of as the conductance of the edge e. Assuming that the set of edges with positive conductances give rise to a unique infinite cluster C∞(ω), we prove a quenched...
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ژورنال
عنوان ژورنال: The Annals of Probability
سال: 2010
ISSN: 0091-1798
DOI: 10.1214/09-aop481