Dissertation/Thesis Abstract

Polymers with the excluded volume effect
by Zhang, Liping, Ph.D., University of California, Irvine, 2011, 67; 3457321
Abstract (Summary)

We study a Gibbs measure Pβ,&thetas;,t, on paths which has a density eβLt/Z β,&thetas;,t with respect to the measure induced by the reflected Brownian motion |Xt| = x + Wt + &thetas;t + L t. We prove that there is a phase transition at the critical value, β = 3&thetas;. For β > 3&thetas;, the paths under this Gibbs measure will be highly localized. In fact, in this regime, the asymptotic distribution of |Xt| is exponential with parameter [special characters omitted]. When β < 3&thetas;, the path is highly delocalized. In this regime, we show that [special characters omitted] has an asymptotically normal distribution. Finally, in the critical phase, β = 3&thetas;, the asymptotic distribution of [special characters omitted] is uniform on [−[special characters omitted]].

Indexing (document details)
Advisor: Cranston, Michael
Commitee: Xin, Jack, Zheng, Weian
School: University of California, Irvine
Department: Mathematics - Ph.D.
School Location: United States -- California
Source: DAI-B 72/08, Dissertation Abstracts International
Subjects: Mathematics, Statistics
Keywords: Excluded volume effect, Gibbs measures
Publication Number: 3457321
ISBN: 978-1-124-67597-8
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