Quenched and annealed critical points in polymer pinning models
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...
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 , ,  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  that the gap is positive, and
extend it to c = 2.
|Item Type:||Working or Discussion Paper (Working Paper)|
|Subjects:||Q Science > QA Mathematics|
|Divisions:||Faculty of 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|
|Number of Pages:||33|
|Status:||Not Peer Reviewed|
|Access rights to Published version:||Open Access|
|Funder:||National Science Foundation (U.S.) (NSF)|
|Grant number:||DMS-0405915 (NSF)|
 Alexander, K.S. (2008). The e®ect of disorder on polymer depinning transitions. Commun. Math. Phys.
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