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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. 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 > 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
Date:	February 2010
Volume:	Vol.20
Number:	No.1
Page Range:	pp. 356-366
Identification Number:	10.1214/09-AAP621
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
Funder:	National Science Foundation (U.S.) (NSF)
Grant number:	DMS-04-05915 (NSF), DMS-08-04934 (NSF)
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URI:	http://wrap.warwick.ac.uk/id/eprint/49157