Table of Contents
ISRN Probability and Statistics
Volume 2013, Article ID 857984, 21 pages
http://dx.doi.org/10.1155/2013/857984
Review Article

Properties of the Parabolic Anderson Model and the Anderson Polymer Model

Mathematics Department, University of California, Irvine, CA 92697-3875, USA

Received 3 September 2012; Accepted 7 November 2012

Academic Editors: M. Campanino and S. Sagitov

Copyright © 2013 Michael Cranston. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

In this article we examine some properties of the solutions of the parabolic Anderson model. In particular we discuss intermittency of the field of solutions of this random partial differential equation, when it occurs and what the field looks like when intermittency doesn't hold. We also explore the behavior of a polymer model created by a Gibbs measure based on solutions to the parabolic Anderson equation.