Limiting behavior of the distance of a random walk

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dc.creatorBerestycki, Nathanael
dc.creatorDurrett, Rick
dc.date2006-04-08
dc.date.accessioned2026-07-07T07:10:40Z
dc.date.available2026-07-07T07:10:40Z
dc.descriptionThis investigation is motivated by a result we proved recently for the random transposition random walk: the distance from the starting point of the walk has a phase transition from a linear regime to a sublinear regime at time $n/2$. Here, we study three new examples. It is trivial that the distance for random walk on the hypercube is smooth and is given by one simple formula. In the case of random adjacent transpositions, we find that there is no phase transition even though the distance has different scalings in three different regimes. In the case of a random 3-regular graph, there is a phase transition from linear growth to a constant equal to the diameter of the graph, at time $3\log_2 n$.
dc.identifierhttps://arxiv.org/abs/math/0604188
dc.identifierhttp://arxiv.org/abs/math/0604188
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/111491
dc.subjectProbability
dc.subjectCombinatorics
dc.subject60G50, 60D05, 60C05
dc.titleLimiting behavior of the distance of a random walk
dc.typetext

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