Excited random walk.
Benjamini, Itai, Wilson, David B. (2003)
Electronic Communications in Probability [electronic only]
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Benjamini, Itai, Wilson, David B. (2003)
Electronic Communications in Probability [electronic only]
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Bérard, Jean, Ramirez, Alejandro (2007)
Electronic Communications in Probability [electronic only]
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Benjamini, Itai, Izkovsky, Roey, Kesten, Harry (2007)
Electronic Journal of Probability [electronic only]
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Krishnapur, Manjunath, Peres, Yuval (2004)
Electronic Communications in Probability [electronic only]
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Zachary, Stan, Foss, S.G. (2006)
Sibirskij Matematicheskij Zhurnal
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Popov, Serguei, Vachkovskaia, Marina (2005)
Electronic Communications in Probability [electronic only]
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Alessandro Berarducci, Pietro Majer, Matteo Novaga (2012)
Fundamenta Mathematicae
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We study the thresholds for the emergence of various properties in random subgraphs of (ℕ, <). In particular, we give sharp sufficient conditions for the existence of (finite or infinite) cliques and paths in a random subgraph. No specific assumption on the probability is made. The main tools are a topological version of Ramsey theory, exchangeability theory and elementary ergodic theory.
Friedrich, Tobias, Sauerwald, Thomas (2010)
The Electronic Journal of Combinatorics [electronic only]
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Jiří Černý, Augusto Teixeira, David Windisch (2011)
Annales de l'I.H.P. Probabilités et statistiques
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We study the trajectory of a simple random walk on a -regular graph with ≥ 3 and locally tree-like structure as the number of vertices grows. Examples of such graphs include random -regular graphs and large girth expanders. For these graphs, we investigate percolative properties of the set of vertices not visited by the walk until time , where > 0 is a fixed positive parameter. We show that this so-called set exhibits a phase transition in in the following sense: there exists...
Berestycki, Nathanael, Durrett, Rick (2008)
Electronic Journal of Probability [electronic only]
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Eckhoff, Maren, Rolles, Silke W.W. (2009)
Electronic Communications in Probability [electronic only]
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