Transition from the annealed to the quenched asymptotics for a random walk on random obstacles

DOI10.1214/009117905000000404zbMath1099.82003arXivmath/0501107OpenAlexW1971510630MaRDI QIDQ2368837

Alejandro F. Ramírez, Gérard Ben Arous, Stanislav Alekseevich Molchanov

Publication date: 28 April 2006

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

Full work available at URL: https://arxiv.org/abs/math/0501107

zbMATH Keywords

principal eigenvaluerandom walkWiener sausageparabolic Anderson modelenlargement of obstacles

Mathematics Subject Classification ID

Interacting particle systems in time-dependent statistical mechanics (82C22) Brownian motion (60J65) Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics (82B44) Probabilistic potential theory (60J45) Random walks, random surfaces, lattice animals, etc. in equilibrium statistical mechanics (82B41)

Related Items (13)

Quenched to annealed transition in the parabolic Anderson problem ⋮ Weak and almost sure limits for the parabolic anderson model with heavy tailed potentials ⋮ Limit theorems for the alloy-type random energy model ⋮ On the association and central limit theorem for solutions of the parabolic Anderson model ⋮ Large fluctuations and transport properties of the Lévy-Lorentz gas ⋮ Properties of the parabolic Anderson model and the Anderson polymer model ⋮ A phase transition in a quenched amorphous ferromagnet ⋮ Biased random walks on Galton-Watson trees with leaves ⋮ Stable limit laws for the parabolic Anderson model between quenched and annealed behaviour ⋮ Infinite server queues in a random fast oscillatory environment ⋮ Limit theorems for time-dependent averages of nonlinear stochastic heat equations ⋮ Extreme value problems in random matrix theory and other disordered systems ⋮ Gibbs states of continuum particle systems with unbounded spins: Existence and uniqueness

Cites Work

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• Parabolic problems for the Anderson model. I: Intermittency and related topics
• Precise large deviation estimates for a one-dimensional random walk in a random environment
• Parabolic problems for the Anderson model. II: Second-order asymptotics and structure of high peaks
• Large deviation principle for random walk in a quenched random environment in the flow speed regime
• Enlargement of obstacles for the simple random walk
• Limit theorems for sums of random exponentials
• On the number of distinct sites visited by a random walk
• Asymptotics for the wiener sausage

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