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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

Dates:

Date	Event
2009	Published

Volume:

Vol.2009

Number:

No.22

Number of Pages:

Status:

Not Peer Reviewed

Access rights to Published version:

Open Access

Funder:

National Science Foundation (U.S.) (NSF)

Grant number:

DMS-0405915 (NSF), DMS-0804934 (NSF)

References:

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