Sharp phase transition in the random stirring model on trees

Details Sharp phase transition in the random stirring model on trees Sharp phase transition in the random stirring model on trees

2012-02-07

arxiv.org/abs/1202.1322v1

Mathematics

Probability

52 pages, six figures. In an appendix, some estimates are refined so that the value of d_0 is improved

Scientific paper

We establish that the phase transition for infinite cycles in the random stirring model on an infinite regular tree of high degree is sharp. That is, we prove that there exists d_0 such that, for any d \geq d_0, the set of parameter values at which the random stirring model on the rooted regular tree with offspring degree d almost surely contains an infinite cycle consists of a semi-infinite interval. The critical point at the left-hand end of this interval is at least 1/d + 1/(2d^2) and at most 1/d + 2/(d^2).

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