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An effective medium approach to the asymptotics of the statistical moments of the parabolic Anderson model and Lifshitz tails
Random medium random Schrodinger operators heat equation with random potential
2011/7/27
An effective medium approach to the asymptotics of the statistical moments of the parabolic Anderson model and Lifshitz tails.
The discrete-time parabolic Anderson model with heavy-tailed potential
Parabolic Anderson Model Directed Polymer Heavy Tailed Potential
2011/2/24
We consider a discrete-time version of the parabolic Anderson model. This may be described as a model for a directed (1+ d)-dimensional polymer interacting with a random potential, which is constant i...
Quenched Lyapunov exponent for the parabolic Anderson model in a dynamic random environment
Quenched Lyapunov exponent parabolic Anderson model
2010/11/9
We continue our study of the parabolic Anderson equation $\partial u/\partial t = \kappa\Delta u + \gamma\xi u$ for the space-time field $u\colon\,\Z^d\times [0,\infty)\to\R$, where $\kappa \in [0,\in...
A scaling limit theorem for the parabolic Anderson model with exponential potential
scaling limit theorem parabolic Anderson model exponential potential
2010/12/13
The parabolic Anderson problem is the Cauchy problem for the heat equation ¶tu(t, z) = D u(t, z)+x (t, z)u(t, z) on (0,¥)×Zd with random potential (x (t, z) : z ∈ Zd ) and localized initial c...