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Reference: Hammond, A, (2013). Sharp phase transition in the random stirring model on trees. Probability Theory and Related Fields, 161 (3-4), 429-448.Citable link to this page:

 

Sharp phase transition in the random stirring model on trees

Abstract: We establish that the phase transition for infinite cycles in the randomstirring model on an infinite regular tree of high degree is sharp. That is, weprove that there exists d_0 such that, for any d \geq d_0, the set of parametervalues at which the random stirring model on the rooted regular tree withoffspring degree d almost surely contains an infinite cycle consists of asemi-infinite interval. The critical point at the left-hand end of thisinterval is at least 1/d + 1/(2d^2) and at most 1/d + 2/(d^2). This version is a major revision, with a much shorter proof. Principal amongthe changes are a reworking of the argument in Section 4 of the old version,which was proposed by a referee, and the use of a simpler means of handling aboundary case, which eliminates the previous Section 6.

Peer Review status:Peer reviewedPublication status:PublishedVersion:Accepted Manuscript Funder: Engineering and Physical Sciences Research Council   Notes:Copyright © 2014. The final publication is available at Springer via http://dx.doi.org/10.1007/s00440-013-0543-7.

Bibliographic Details

Publisher: Springer Berlin Heidelberg

Publisher Website: http://www.springer.com/

Journal: Probability Theory and Related Fieldssee more from them

Publication Website: http://link.springer.com/journal/440

Issue Date: 2013

pages:429-448Identifiers

Urn: uuid:907aaa45-4f94-4d66-bbe1-0416b2ac10f7

Source identifier: 254319

Eissn: 1432-2064

Doi: https://doi.org/10.1007/s00440-013-0543-7

Issn: 0178-8051 Item Description

Type: Journal article;

Language: eng

Version: Accepted ManuscriptKeywords: spatial random permutations random stirring process random interchange model primary 60K35 Tiny URL: pubs:254319

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Autor: Hammond, A - institutionUniversity of Oxford Oxford, MPLS, Statistics - - - - Bibliographic Details Publisher: Springer Berlin He

Fuente: https://ora.ox.ac.uk/objects/uuid:907aaa45-4f94-4d66-bbe1-0416b2ac10f7



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