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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 (2009) Equality of critical points for polymer depinning transitions with loop exponent one. Working Paper. Coventry: University of Warwick. Centre for Research in Statistical Methodology. Working papers, Vol.2009 (No.22).

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Abstract
We consider a polymer with configuration modeled 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:  Working or Discussion Paper (Working Paper) 

Subjects:  Q Science > QA Mathematics 
Divisions:  Faculty of Science > Statistics 
Library of Congress Subject Headings (LCSH):  Polymers  Mathematical models, Markov processes 
Series Name:  Working papers 
Publisher:  University of Warwick. Centre for Research in Statistical Methodology 
Place of Publication:  Coventry 
Official Date:  2009 
Volume:  Vol.2009 
Number:  No.22 
Number of Pages:  10 
Status:  Not Peer Reviewed 
Access rights to Published version:  Open Access 
Funder:  National Science Foundation (U.S.) (NSF) 
Grant number:  DMS0405915 (NSF), DMS0804934 (NSF) 
References:  [Al08] Alexander, K. S. (2008). The e_ect of disorder on polymer depinning transitions. Commun. 
URI:  http://wrap.warwick.ac.uk/id/eprint/35210 
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