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Equality of critical points for polymer depinning transitions with loop exponent one
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Alexander, Kenneth S. and Zygouras, Nikos (2010) Equality of critical points for polymer depinning transitions with loop exponent one. Annals of Applied Probability, Vol.20 (No.1). pp. 356-366. doi:10.1214/09-AAP621 ISSN 1050-5164.
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Official URL: http://dx.doi.org/10.1214/09-AAP621
Abstract
We consider a polymer with configuration modelled by the trajectory of a Markov chain, interacting with a potential of form u+Vn when it visits a particular state 0 at time n, with {Vn} representing i.i.d. quenched disorder. There is a critical value of u above which the polymer is pinned by the potential. A particular case not covered in a number of previous studies is that of loop exponent one, in which the probability of an excursion of length n takes the form φ(n)/n for some slowly varying φ; this includes simple random walk in two dimensions. We show that in this case, at all temperatures, the critical values of u in the quenched and annealed models are equal, in contrast to all other loop exponents, for which these critical values are known to differ, at least at low temperatures.
| Item Type: | Journal Article | ||||
|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||
| Library of Congress Subject Headings (LCSH): | Polymers -- Mathematical models, Markov processes | ||||
| Journal or Publication Title: | Annals of Applied Probability | ||||
| Publisher: | Institute of Mathematical Statistics | ||||
| ISSN: | 1050-5164 | ||||
| Official Date: | February 2010 | ||||
| Dates: |
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| Volume: | Vol.20 | ||||
| Number: | No.1 | ||||
| Page Range: | pp. 356-366 | ||||
| DOI: | 10.1214/09-AAP621 | ||||
| Status: | Peer Reviewed | ||||
| Publication Status: | Published | ||||
| Access rights to Published version: | Restricted or Subscription Access | ||||
| Date of first compliant deposit: | 22 December 2015 | ||||
| Date of first compliant Open Access: | 22 December 2015 | ||||
| Funder: | National Science Foundation (U.S.) (NSF) | ||||
| Grant number: | DMS-04-05915 (NSF), DMS-08-04934 (NSF) |
Data sourced from Thomson Reuters' Web of Knowledge
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