A two cities theorem for the parabolic Anderson model

DOI10.1214/08-AOP405zbMath1183.60024arXiv1102.4921OpenAlexW2030512597MaRDI QIDQ1011160

Wolfgang König, Hubert Lacoin, Peter Mörters, Nadezda A. Sidorova

Publication date: 8 April 2009

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1102.4921

zbMATH Keywords

random potentialFeynman-Kac formulalocalizationheavy tailPareto distributionintermittencypinning effectAnderson Hamiltonianparabolic Anderson problempolynomial tail

Mathematics Subject Classification ID

Random operators and equations (aspects of stochastic analysis) (60H25) Large deviations (60F10) Dynamics of disordered systems (random Ising systems, etc.) in time-dependent statistical mechanics (82C44)

Related Items (24)

Scaling limit and ageing for branching random walk in Pareto environment ⋮ Localisation in the Bouchaud-Anderson model ⋮ Mass concentration and aging in the parabolic Anderson model with doubly-exponential tails ⋮ Delocalising the parabolic Anderson model through partial duplication of the potential ⋮ Localization for random walks among random obstacles in a single Euclidean ball ⋮ The parabolic Anderson model on the hypercube ⋮ The discrete-time parabolic Anderson model with heavy-tailed potential ⋮ Localisation and ageing in the parabolic Anderson model with Weibull potential ⋮ Some ergodic theorems for a parabolic Anderson model ⋮ Ageing in the parabolic Anderson model ⋮ An ergodic theorem of a parabolic Anderson model driven by Lévy noise ⋮ Eigenvalue order statistics for random Schrödinger operators with doubly-exponential tails ⋮ Parabolic Anderson model on critical Galton-Watson trees in a Pareto environment ⋮ Properties of the parabolic Anderson model and the Anderson polymer model ⋮ An asymptotic theory for randomly forced discrete nonlinear heat equations ⋮ Overlaps and pathwise localization in the Anderson polymer model ⋮ Distribution of the random walk conditioned on survival among quenched Bernoulli obstacles ⋮ Extremal theory for spectrum of random discrete Schrödinger operator. II. Distributions with heavy tails ⋮ The Bouchaud-Anderson model with double-exponential potential ⋮ On the stochastic heat equation with spatially-colored random forcing ⋮ A new phase transition in the parabolic Anderson model with partially duplicated potential ⋮ Intermittency for branching random walk in Pareto environment ⋮ Poly-logarithmic localization for random walks among random obstacles ⋮ Non-directed polymers in heavy-tail random environment in dimension \(d\geq 2\)

Cites Work

• Intermittency in a catalytic random medium
• The universality classes in the parabolic Anderson model
• Parabolic problems for the Anderson model. I: Intermittency and related topics
• Exact asymptotics in a mean field model with random potential
• Localization and selection in a mean field branching random walk in a random environment
• Geometric characterization of intermittency in the parabolic Anderson model
• Weak and almost sure limits for the parabolic anderson model with heavy tailed potentials
• Parabolic Anderson problem and intermittency
• Brownian intersection local times: Exponential moments and law of large masses
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