Geometric characterization of intermittency in the parabolic Anderson model

DOI10.1214/009117906000000764zbMath1126.60091arXivmath/0507585OpenAlexW2065093600MaRDI QIDQ2371945

Stanislav Alekseevich Molchanov, Wolfgang König, Jürgen Gärtner

Publication date: 9 July 2007

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

Full work available at URL: https://arxiv.org/abs/math/0507585

zbMATH Keywords

random environmentparabolic Anderson modelintermittencyquenched asymptoticsheat equation with random potential

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Other physical applications of random processes (60K40) Random operators and equations (aspects of stochastic analysis) (60H25) Large deviations (60F10) Random linear operators (47B80) Dynamics of disordered systems (random Ising systems, etc.) in time-dependent statistical mechanics (82C44)

Related Items (35)

INTERMITTENCY AND MULTISCALING IN LIMIT THEOREMS ⋮ Spread of a catalytic branching random walk on a multidimensional lattice ⋮ Weak and almost sure limits for the parabolic anderson model with heavy tailed potentials ⋮ 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 ⋮ The parabolic Anderson model on a Galton-Watson tree revisited ⋮ Intermittency in a catalytic random medium ⋮ Localization for random walks among random obstacles in a single Euclidean ball ⋮ Limit theorems for the alloy-type random energy model ⋮ The parabolic Anderson model on the hypercube ⋮ The universality classes in the parabolic Anderson model ⋮ Intermittency in the small-time behavior of Lévy processes ⋮ Branching processes with lattice spatial dynamics and a finite set of particle generation centers ⋮ Localisation and ageing in the parabolic Anderson model with Weibull potential ⋮ The unusual properties of aggregated superpositions of Ornstein-Uhlenbeck type processes ⋮ The stochastic heat equation with multiplicative Lévy noise: existence, moments, and intermittency ⋮ On the existence and position of the farthest peaks of a family of stochastic heat and wave equations ⋮ Eigenvalue order statistics for random Schrödinger operators with doubly-exponential tails ⋮ Properties of the parabolic Anderson model and the Anderson polymer model ⋮ Large deviations for a symmetric branching random walk on a multidimensional lattice ⋮ Extremal theory for spectrum of random discrete Schrödinger operator. I: Asymptotic expansion formulas ⋮ The Bouchaud-Anderson model with double-exponential potential ⋮ The parabolic Anderson model on a Galton-Watson tree ⋮ Symmetric Branching Walks in Homogeneous and Non Homogeneous Random Environments ⋮ Intermittency of superpositions of Ornstein-Uhlenbeck type processes ⋮ A new phase transition in the parabolic Anderson model with partially duplicated potential ⋮ Intermittency properties in a hyperbolic Anderson problem ⋮ Lyapunov exponents of the half-line SHE ⋮ Potential confinement property of the parabolic Anderson model ⋮ Fractional moments of the stochastic heat equation ⋮ A two cities theorem for the parabolic Anderson model ⋮ Intermittency and Chaos for a Nonlinear Stochastic Wave Equation in Dimension 1 ⋮ Poly-logarithmic localization for random walks among random obstacles ⋮ KPZ equation tails for general initial data

Cites Work

• The universality classes in the parabolic Anderson model
• Parabolic problems for the Anderson model. I: Intermittency and related topics
• Correlation structure of intermittency in the parabolic Anderson model
• Parabolic problems for the Anderson model. II: Second-order asymptotics and structure of high peaks
• Moment asymptotics for the continuous parabolic Anderson model.
• Almost sure asymptotics for the continuous parabolic Anderson model
• Long-time tails in the parabolic Anderson model with bounded potential
• Parabolic Anderson problem and intermittency
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