Anomalous heat-kernel decay for random walk among bounded random conductances

DOI10.1214/07-AIHP126zbMath1187.60034arXivmath/0611666OpenAlexW3099524846MaRDI QIDQ731675

C. E. Hoffman, Marek Biskup, Gady Kozma, Noam Berger

Publication date: 8 October 2009

Published in: Annales de l'Institut Henri Poincaré. Probabilités et Statistiques (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0611666

zbMATH Keywords

simple random walkrandom environments

Mathematics Subject Classification ID

Sums of independent random variables; random walks (60G50) Processes in random environments (60K37) Dynamics of random walks, random surfaces, lattice animals, etc. in time-dependent statistical mechanics (82C41)

Related Items

Harnack inequalities on weighted graphs and some applications to the random conductance model, Isoperimetry in supercritical bond percolation in dimensions three and higher, Un théorème limite central local en environnement aléatoire stationnaire de conductances sur Z, A parabolic Harnack principle for balanced difference equations in random environments, Isoperimetry in Two-Dimensional Percolation, Quenched invariance principle for simple random walk on clusters in correlated percolation models, Intrinsic isoperimetry of the giant component of supercritical bond percolation in dimension two, Localization of the principal Dirichlet eigenvector in the heavy-tailed random conductance model, Local limit theorems for the random conductance model and applications to the Ginzburg-Landau \(\nabla \phi\) interface model, Invariance principle for the random conductance model, Invariance principle for Mott variable range hopping and other walks on point processes, Quenched local limit theorem for random walks among time-dependent ergodic degenerate weights, Disorder, entropy and harmonic functions, Anchored Nash inequalities and heat kernel bounds for static and dynamic degenerate environments, Large fluctuations and transport properties of the Lévy-Lorentz gas, Scaling limit for a class of gradient fields with nonconvex potentials, Trapping in the random conductance model, Random mass splitting and a quenched invariance principle, Harnack inequalities and local central limit theorem for the polynomial lower tail random conductance model, Green kernel asymptotics for two-dimensional random walks under random conductances, Recent progress on the random conductance model, Discrete fractal dimensions of the ranges of random walks in \(\mathbb Z^d\) associate with random conductances, The speed of a biased random walk on a percolation cluster at high density, Quenched invariance principle for simple random walk on discrete point processes, Kantorovich distance in the martingale CLT and quantitative homogenization of parabolic equations with random coefficients, Heat kernel estimates and intrinsic metric for random walks with general speed measure under degenerate conductances, Interplay of analysis and probability in applied mathematics. Abstracts from the workshop held February 11--17, 2018, Seven-dimensional forest fires, On heat kernel decay for the random conductance model, Quenched invariance principles for random walks with random conductances, Heat-kernel estimates for random walk among random conductances with heavy tail, Invariance principle for the random conductance model with unbounded conductances, Existence of the anchored isoperimetric profile in supercritical bond percolation in dimension two and higher, Random walks in random conductances: decoupling and spread of infection, Heat kernel decay on a stationary environment of conductances, Quantitative homogenization of the parabolic and elliptic Green's functions on percolation clusters, Quenched invariance principle for a class of random conductance models with long-range jumps, SPDE limit of weakly inhomogeneous ASEP, Lower Gaussian heat kernel bounds for the random conductance model in a degenerate ergodic environment, Random conductance models with stable-like jumps: heat kernel estimates and Harnack inequalities, Random walks on discrete point processes, Absolutely continuous spectrum implies ballistic transport for quantum particles in a random potential on tree graphs

Cites Work

• Unnamed Item
• An invariance principle for reversible Markov processes. Applications to random motions in random environments
• On symmetric random walks with random conductances on \(\mathbb Z^d\)
• Mixing time bounds via the spectral profile
• Quenched invariance principle for simple random walk on percolation clusters
• A note on percolation on \(\mathbb Z^d\): isoperimetric profile via exponential cluster repulsion
• Isoperimetric inequalities and Markov chains
• Central limit theorem for additive functionals of reversible Markov processes and applications to simple exclusions
• Upper bounds for symmetric Markov transition functions
• Parabolic Harnack inequality and estimates of Markov chains on graphs
• Random walk on the infinite cluster of the percolation model
• Heat kernel upper bounds on a complete non-compact manifold
• On the mixing time of a simple random walk on the super critical percolation cluster
• Return probabilities of a simple random walk on percolation clusters
• Random walks on supercritical percolation clusters
• Isoperimetry and heat kernel decay on percolation clusters.
• Quenched invariance principles for walks on clusters of percolation or among random conduc\-tances
• Functional CLT for random walk among bounded random conductances
• Quenched invariance principles for random walks with random conductances
• On the chemical distance for supercritical Bernoulli percolation
• Evolving sets, mixing and heat kernel bounds
• Sur le nombre de points visités par une marche aléatoire sur un amas infini de percolation
• Percolation
• Quenched invariance principles for random walks on percolation clusters