dc.contributor.author Hutchcroft, TM dc.date.accessioned 2019-01-18T00:31:01Z dc.date.available 2019-01-18T00:31:01Z dc.date.issued 2019 dc.identifier.issn 0091-1798 dc.identifier.uri https://www.repository.cam.ac.uk/handle/1810/288163 dc.description.abstract We 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.sponsorship Microsoft Research dc.publisher Institute of Mathematical Statistics dc.rights All rights reserved dc.title Self-avoiding walk on nonunimodular transitive graphs dc.type Article prism.endingPage 2829 prism.issueIdentifier 5 prism.publicationName Annals of Probability prism.startingPage 2801 prism.volume 47 dc.identifier.doi 10.17863/CAM.35479 dcterms.dateAccepted 2018-10-31 rioxxterms.versionofrecord 10.1214/18-AOP1322 rioxxterms.version VoR rioxxterms.licenseref.uri http://www.rioxx.net/licenses/all-rights-reserved rioxxterms.licenseref.startdate 2018-10-31 dc.contributor.orcid Hutchcroft, Thomas [0000-0003-0061-593X] dc.identifier.eissn 2168-894X rioxxterms.type Journal Article/Review cam.issuedOnline 2019-10-22 cam.orpheus.success Mon Jul 20 07:55:39 BST 2020 - The item has an open VoR version. cam.orpheus.counter 12 rioxxterms.freetoread.startdate 2100-01-01
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