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).

Preview

PDF WRAP_Alexander_09-22w.pdf - Published Version - Requires a PDF viewer. Download (432Kb)

Request Changes to record.

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:	10
Institution:	University of Warwick
Status:	Not Peer Reviewed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)

Request changes or add full text files to a record

Repository staff actions (login required)

View Item

Downloads