Logarithmic Components of the Vacant Set for Random Walk on a Discrete Torus
نویسندگان
چکیده
منابع مشابه
Logarithmic components of the vacant set for random walk on a discrete torus
This work continues the investigation, initiated in a recent work by Benjamini and Sznitman, of percolative properties of the set of points not visited by a random walk on the discrete torus (Z/NZ)d up to time uNd in high dimension d. If u > 0 is chosen sufficiently small it has been shown that with overwhelming probability this vacant set contains a unique giant component containing segments o...
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We consider random walk on a discrete torus E of side-length N , in sufficiently high dimension d. We investigate the percolative properties of the vacant set corresponding to the collection of sites which have not been visited by the walk up to time uNd. We show that when u is chosen small, as N tends to infinity, there is with overwhelming probability a unique connected component in the vacan...
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Abstract. We consider a simple random walk on a discrete torus (Z/NZ) with dimension d ≥ 3 and large side length N . For a fixed constant u ≥ 0, we study the percolative properties of the vacant set, consisting of the set of vertices not visited by the random walk in its first [uN] steps. We prove the existence of two distinct phases of the vacant set in the following sense: if u > 0 is chosen ...
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ژورنال
عنوان ژورنال: Electronic Journal of Probability
سال: 2008
ISSN: 1083-6489
DOI: 10.1214/ejp.v13-506