Critical window for the vacant set left by random walk on random regular graphs
نویسندگان
چکیده
منابع مشابه
Critical window for the vacant set left by random walk on random regular graphs
We consider the simple random walk on a random d-regular graph with n vertices, and investigate percolative properties of the set of vertices not visited by the walk until time un, where u > 0 is a fixed positive parameter. It was shown in [ČTW11] that this so-called vacant set exhibits a phase transition at u = u?: there is a giant component if u < u? and only small components when u > u?. In ...
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We consider a random walk on a d-regular graph G where d → ∞ and G satisfies certain conditions. Our prime example is the d-dimensional hypercube, which has n = 2 vertices. We explore the likely component structure of the vacant set, i.e. the set of unvisited vertices. Let Λ(t) be the subgraph induced by the vacant set of the walk at step t. We show that if certain conditions are satisfied then...
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ژورنال
عنوان ژورنال: Random Structures & Algorithms
سال: 2012
ISSN: 1042-9832
DOI: 10.1002/rsa.20425