Results 1  10
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17
A lower bound on the disconnection time of a discrete cylinder
 In and Out of Equilibrium 2, Birkh"auser
, 2008
"... ..."
RANDOM WALK ON A DISCRETE TORUS AND RANDOM INTERLACEMENTS
 ELECTRONIC COMMUNICATIONS IN PROBABILITY
, 2008
"... We investigate the relation between the local picture left by the trajectory of a simple random walk on the torus (Z/NZ) d, d ≥ 3, until uN d time steps, u> 0, and the model of random interlacements recently introduced by Sznitman [9]. In particular, we show that for large N, the joint distribution ..."
Abstract

Cited by 19 (3 self)
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We investigate the relation between the local picture left by the trajectory of a simple random walk on the torus (Z/NZ) d, d ≥ 3, until uN d time steps, u> 0, and the model of random interlacements recently introduced by Sznitman [9]. In particular, we show that for large N, the joint distribution of the local pictures in the neighborhoods of finitely many distant points left by the walk up to time uN d converges to independent copies of the random interlacement at level u.
On the uniqueness of the infinite cluster of the vacant set of random interlacements
 ANN. APPL. PROBAB
, 2009
"... We consider the model of random interlacements on Z d introduced in Sznitman [Vacant set of random interlacements and percolation (2007) preprint]. For this model, we prove the uniqueness of the infinite component of the vacant set. As a consequence, we derive the continuity in u of the probability ..."
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Cited by 13 (2 self)
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We consider the model of random interlacements on Z d introduced in Sznitman [Vacant set of random interlacements and percolation (2007) preprint]. For this model, we prove the uniqueness of the infinite component of the vacant set. As a consequence, we derive the continuity in u of the probability that the origin belongs to the infinite component of the vacant set at level u in the supercritical phase u<u∗.
On the Rank of Random
 Matrices”, Random Structures and Algorithms 16(2
, 2000
"... structure induced by a random walk on a ..."
Deterministic random walks
 In Proceedings of the Workshop on Analytic Algorithmics and Combinatorics
, 2006
"... structure of the vacant set induced by a ..."
RANDOM PLANAR METRICS
"... Abstract. A discussion regarding aspects of several quite different random planar metrics and related topics is presented. 1. ..."
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Cited by 4 (1 self)
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Abstract. A discussion regarding aspects of several quite different random planar metrics and related topics is presented. 1.
ON THE DISCONNECTION OF A DISCRETE CYLINDER BY A BIASED RANDOM WALK
, 2008
"... We consider a random walk on the discrete cylinder (Z/NZ) d ×Z, d ≥ 3 with drift N−dα in the Zdirection and investigate the large Nbehavior of the disconnection time T disc N, defined as the first time when the trajectory of the random walk disconnects the cylinder into two infinite components. We ..."
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Cited by 3 (1 self)
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We consider a random walk on the discrete cylinder (Z/NZ) d ×Z, d ≥ 3 with drift N−dα in the Zdirection and investigate the large Nbehavior of the disconnection time T disc N, defined as the first time when the trajectory of the random walk disconnects the cylinder into two infinite components. We prove that, as long as the drift exponent α is strictly greater than 1, the asymptotic behavior of T disc N remains N2d+o(1) , as in the unbiased case considered by Dembo and Sznitman, whereas for α<1, the asymptotic behavior of T disc N becomes exponential in N.
DECOUPLING INEQUALITIES AND INTERLACEMENT PERCOLATION ON G × Z
, 2010
"... We study the percolative properties of random interlacements on G×Z, where G is a weighted graph satisfying certain subGaussian estimates attached to the parameters α> 1 and 2 ≤ β ≤ α + 1. We develop decoupling inequalities, which are a key tool in showing that the critical level u ∗ for the percol ..."
Abstract

Cited by 3 (1 self)
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We study the percolative properties of random interlacements on G×Z, where G is a weighted graph satisfying certain subGaussian estimates attached to the parameters α> 1 and 2 ≤ β ≤ α + 1. We develop decoupling inequalities, which are a key tool in showing that the critical level u ∗ for the percolation of the vacant set of random interlacements is always finite in our setup, and that it is positive when α ≥ 1 + β 2. We also obtain several stretched exponential controls both in the percolative and nonpercolative phases of the model. Even in the case where G = Zd, d ≥ 2, several of these results are new.