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dc.contributor.authorHutchcroft, TM
dc.date.accessioned2019-01-18T00:31:01Z
dc.date.available2019-01-18T00:31:01Z
dc.date.issued2019
dc.identifier.issn0091-1798
dc.identifier.urihttps://www.repository.cam.ac.uk/handle/1810/288163
dc.description.abstractWe study self-avoiding walk on graphs whose automorphism group has a transitive nonunimodular subgroup. We prove that self-avoiding walk is ballistic, that the bubble diagram converges at criticality, and that the critical two-point function decays exponentially in the distance from the origin. This implies that the critical exponent governing the susceptibility takes its mean-field value, and hence that the number of self-avoiding walks of length $n$ is comparable to the $n$th power of the connective constant. We also prove that the same results hold for a large class of repulsive walk models with a self-intersection based interaction, including the weakly self-avoiding walk. All these results apply in particular to the product $T_k \times \Z^d$ of a $k$-regular tree ($k\geq 3$) with $\Z^d$, for which these results were previously only known for large $k$.
dc.description.sponsorshipMicrosoft Research
dc.publisherInstitute of Mathematical Statistics
dc.rightsAll rights reserved
dc.titleSelf-avoiding walk on nonunimodular transitive graphs
dc.typeArticle
prism.endingPage2829
prism.issueIdentifier5
prism.publicationNameAnnals of Probability
prism.startingPage2801
prism.volume47
dc.identifier.doi10.17863/CAM.35479
dcterms.dateAccepted2018-10-31
rioxxterms.versionofrecord10.1214/18-AOP1322
rioxxterms.versionVoR
rioxxterms.licenseref.urihttp://www.rioxx.net/licenses/all-rights-reserved
rioxxterms.licenseref.startdate2018-10-31
dc.contributor.orcidHutchcroft, Thomas [0000-0003-0061-593X]
dc.identifier.eissn2168-894X
rioxxterms.typeJournal Article/Review
cam.issuedOnline2019-10-22
cam.orpheus.successMon Jul 20 07:55:39 BST 2020 - The item has an open VoR version.
cam.orpheus.counter12
rioxxterms.freetoread.startdate2100-01-01


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