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]].
|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|
|Keywords:||Excluded volume effect, Gibbs measures|
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