Quenched asymptotics for Brownian motion of renormalized Poisson potential and for the related parabolic Anderson models

DOI10.1214/11-AOP655zbMath1259.60094arXiv1207.6483MaRDI QIDQ439874

Xia Chen

Publication date: 17 August 2012

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

Full work available at URL: https://arxiv.org/abs/1207.6483

zbMATH Keywords

renormalizationlarge deviationsPoisson fieldparabolic Anderson modelFeynman-Kac representationBrownian motion in Poisson potential

Mathematics Subject Classification ID

Brownian motion (60J65) Other physical applications of random processes (60K40) Large deviations (60F10) Processes in random environments (60K37) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55)

Related Items

Brownian motion in attenuated or renormalized inverse-square Poisson potential ⋮ Interpolating the stochastic heat and wave equations with time-independent noise: solvability and exact asymptotics ⋮ Almost surely time-space intermittency for the parabolic Anderson model with a log-correlated Gaussian field ⋮ Feynman–Kac formula for parabolic Anderson model in Gaussian potential and fractional white noise ⋮ Exponential asymptotics for time-space Hamiltonians ⋮ 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 ⋮ Brownian motion and parabolic Anderson model in a renormalized Poisson potential ⋮ Quenched asymptotics for Brownian motion in generalized Gaussian potential ⋮ Large deviations for Brownian motion in a random 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 ⋮ Phase transitions in asymptotically singular Anderson Hamiltonian and parabolic model ⋮ Quenched asymptotics for symmetric Lévy processes interacting with Poissonian fields

Cites Work

• Unnamed Item
• Unnamed Item
• Brownian motion and parabolic Anderson model in a renormalized Poisson potential
• Quenched law of large numbers for branching Brownian motion in a random medium
• Large deviations for Riesz potentials of additive processes
• The universality classes in the parabolic Anderson model
• Parabolic problems for the Anderson model. I: Intermittency and related topics
• Sharp asymptotics for the partition function of some continuous-time directed polymers
• Almost sure exponential behavior of a directed polymer in a fractional Brownian environment
• Intermittency properties in a hyperbolic Anderson problem
• Brownian asymptotics in a Poissonian environment
• 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
• Stationary parabolic Anderson model and intermittency
• Brownian survival among Gibbsian traps
• Weak and almost sure limits for the parabolic anderson model with heavy tailed potentials
• Sharp estimation of the almost-sure Lyapunov exponent for the Anderson model in continuous space
• Lyapunov exponent for the parabolic Anderson model with Lévy noise
• Parabolic Anderson problem and intermittency
• Almost-sure exponential behavior of a stochastic anderson model with continuous space parameter
• Sharp upper bound on the almost-sure exponential behavior of a stochastic parabolic partial differential equation

This page was built for publication: Quenched asymptotics for Brownian motion of renormalized Poisson potential and for the related parabolic Anderson models