Moment asymptotics for the continuous parabolic Anderson model.

DOI10.1214/aoap/1019737669zbMath1171.60359OpenAlexW2025703969MaRDI QIDQ1578613

Jürgen Gärtner, Wolfgang König

Publication date: 4 September 2000

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

Full work available at URL: https://doi.org/10.1214/aoap/1019737669

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) 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 (25)

Long-time tails in the parabolic Anderson model with bounded potential ⋮ Continuous integral kernels for unbounded Schrödinger semigroups and their spectral projections ⋮ Geometric characterization of intermittency in the parabolic Anderson model ⋮ Intermittency in a catalytic random medium ⋮ Annealed Brownian motion in a heavy tailed Poissonian potential ⋮ The universality classes in the parabolic Anderson model ⋮ Moment intermittency in the PAM with asymptotically singular noise ⋮ Asymptotic of the smallest eigenvalues of the continuous Anderson Hamiltonian in \(d\le 3\) ⋮ Moment asymptotics for the parabolic Anderson problem with a perturbed lattice potential ⋮ Feynman–Kac formula for parabolic Anderson model in Gaussian potential and fractional white noise ⋮ Annealed asymptotics for Brownian motion of renormalized potential in mobile random medium ⋮ Asymptotics of negative exponential moments for annealed Brownian motion in a renormalized Poisson potential ⋮ Quenched asymptotics for Brownian motion of renormalized Poisson potential and for the related parabolic Anderson models ⋮ Brownian motion and parabolic Anderson model in a renormalized Poisson potential ⋮ Quenched asymptotics for Brownian motion in generalized Gaussian potential ⋮ The mild and weak solutions of a stochastic parabolic Anderson equation ⋮ Quenched asymptotics for a 1-d stochastic heat equation driven by a rough spatial noise ⋮ Mild solution to parabolic Anderson model in Gaussian and Poisson potential ⋮ Quenched tail estimate for the random walk in random scenery and in random layered conductance ⋮ Precise high moment asymptotics for parabolic Anderson model with log-correlated Gaussian field ⋮ Asymptotics of the eigenvalues of the Anderson Hamiltonian with white noise potential in two dimensions ⋮ Spectral rigidity of random Schrödinger operators via Feynman-Kac formulas ⋮ ASYMPTOTIC BEHAVIOR OF THE INTEGRATED DENSITY OF STATES FOR RANDOM POINT FIELDS ASSOCIATED WITH CERTAIN FREDHOLM DETERMINANTS ⋮ Phase transitions in asymptotically singular Anderson Hamiltonian and parabolic model ⋮ Quenched large deviations for diffusions in a random Gaussian shear flow drift.

Cites Work

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• Parabolic problems for the Anderson model. I: Intermittency and related topics
• Invariance principle and empirical mean large deviations of the critical Ornstein-Uhlenbeck process
• Correlation structure of intermittency in the parabolic Anderson model
• Parabolic problems for the Anderson model. II: Second-order asymptotics and structure of high peaks
• Almost sure asymptotics for the continuous parabolic Anderson model
• Stationary parabolic Anderson model and intermittency
• Parabolic Anderson problem and intermittency

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