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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. 356366. ISSN 10505164

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Official URL: http://dx.doi.org/10.1214/09AAP621
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:  10505164  
Official Date:  February 2010  
Dates: 


Volume:  Vol.20  
Number:  No.1  
Page Range:  pp. 356366  
Identifier:  10.1214/09AAP621  
Status:  Peer Reviewed  
Publication Status:  Published  
Access rights to Published version:  Restricted or Subscription Access  
Funder:  National Science Foundation (U.S.) (NSF)  
Grant number:  DMS0405915 (NSF), DMS0804934 (NSF)  
References:  [1] ALEXANDER, K. S. (2008). The effect of disorder on polymer depinning transitions. Comm. 

URI:  http://wrap.warwick.ac.uk/id/eprint/49157 
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