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Quenched and annealed critical points in polymer pinning models
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Alexander, Kenneth S. and Zygouras, Nikos (2009) Quenched and annealed critical points in polymer pinning models. Working Paper. Coventry: University of Warwick. Centre for Research in Statistical Methodology. Working papers, Vol.2009 (No.21).
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Official URL: http://www2.warwick.ac.uk/fac/sci/statistics/crism...
Abstract
We consider a polymer with configuration modeled by the path of a Markov
chain, interacting with a potential u+Vn which the chain encounters when it visits a special
state 0 at time n. The disorder (Vn) is a fixed realization of an i.i.d. sequence. The polymer
is pinned, i.e. the chain spends a positive fraction of its time at state 0, when u exceeds
a critical value. We assume that for the Markov chain in the absence of the potential, the
probability of an excursion from 0 of length n has the form n-cφ(n) with c ≥ 1 and φ slowly
varying. Comparing to the corresponding annealed system, in which the Vn are effectively
replaced by a constant, it was shown in [1], [4], [11] that the quenched and annealed critical
points differ at all temperatures for 3/2 < c < 2 and c > 2, but only at low temperatures
for c < 3/2. For high temperatures and 3/2 < c < 2 we establish the exact order of the gap
between critical points, as a function of temperature. For the borderline case c = 3/2 we
show that the gap is positive provided φ(n) -> 0 as n -> ∞, and for c > 3/2 with arbitrary
temperature we provide an alternate proof of the result in [4] that the gap is positive, and
extend it to c = 2.
Item Type: | Working or Discussion Paper (Working Paper) | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||
Library of Congress Subject Headings (LCSH): | Markov processes, Critical point | ||||
Series Name: | Working papers | ||||
Publisher: | University of Warwick. Centre for Research in Statistical Methodology | ||||
Place of Publication: | Coventry | ||||
Official Date: | 2009 | ||||
Dates: |
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Volume: | Vol.2009 | ||||
Number: | No.21 | ||||
Number of Pages: | 33 | ||||
Institution: | University of Warwick | ||||
Status: | Not Peer Reviewed | ||||
Access rights to Published version: | Open Access (Creative Commons) | ||||
Date of first compliant deposit: | 1 August 2016 | ||||
Date of first compliant Open Access: | 1 August 2016 | ||||
Funder: | National Science Foundation (U.S.) (NSF) | ||||
Grant number: | DMS-0405915 (NSF) |
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