Recent progress on the random conductance model
From MaRDI portal
Publication:431513
DOI10.1214/11-PS190zbMath1245.60098arXiv1112.0104OpenAlexW1498420657MaRDI QIDQ431513
Publication date: 28 June 2012
Published in: Probability Surveys (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1112.0104
homogenizationheat kernel boundscorrectorquenched invariance principlerandom conductance modeleffective resistivityelliptic environment
Probabilistic potential theory (60J45) Percolation (82B43) Processes in random environments (60K37) Functional limit theorems; invariance principles (60F17) Homogenization for problems in thermodynamics and heat transfer (80M40)
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Cites Work
- Random Walks on Infinite Graphs and Groups
- Quenched invariance principles for random walks on percolation clusters
- The Random-Cluster Model
- Bounds for the fundamental solution of a parabolic equation
- On a Theorem of Skorohod
- Martingale Central Limit Theorems
- Probability
- Large deviations
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Quantitative version of the Kipnis-Varadhan theorem and Monte Carlo approximation of homogenized coefficients
- Invariance principle for the random conductance model
- Invariance principle for Mott variable range hopping and other walks on point processes
- A quantitative central limit theorem for the random walk among random conductances
- Random walks on Galton-Watson trees with random conductances
- Harmonic deformation of Delaunay triangulations
- Ballistic regime for random walks in random environment with unbounded jumps and Knudsen billiards
- Decay of covariances, uniqueness of ergodic component and scaling limit for a class of \(\nabla\phi\) systems with non-convex potential
- An optimal variance estimate in stochastic homogenization of discrete elliptic equations
- Diffusive limits on the Penrose tiling
- Contour lines of the two-dimensional discrete Gaussian free field
- Scaling limit for a class of gradient fields with nonconvex potentials
- Recursions and tightness for the maximum of the discrete, two dimensional Gaussian free field
- Standard spectral dimension for the polynomial lower tail random conductances model
- A central limit theorem for random walk in a random environment on a marked Galton-Watson tree.
- On two-dimensional random walk among heavy-tailed conductances
- Convergence to fractional kinetics for random walks associated with unbounded conductances
- Quenched invariance principle for random walks in balanced random environment
- Loop-erased random walk and Poisson kernel on planar graphs
- Strict convexity of the free energy for a class of non-convex gradient models
- Anomalous heat-kernel decay for random walk among bounded random conductances
- An invariance principle for reversible Markov processes. Applications to random motions in random environments
- On symmetric random walks with random conductances on \(\mathbb Z^d\)
- Central limit theorem for stationary linear processes
- Quenched invariance principle for simple random walk on percolation clusters
- Disorder, entropy and harmonic functions
- Thick points of the Gaussian free field
- Localization and delocalization of random interfaces
- The Alexander-Orbach conjecture holds in high dimensions
- A note on percolation on \(\mathbb Z^d\): isoperimetric profile via exponential cluster repulsion
- Parabolic Harnack inequality and local limit theorem for percolation clusters
- The diffusion limit for reversible jump processes on \(Z^ m\) with ergodic random bond conductivities
- Isoperimetric inequalities and Markov chains
- On birth and death processes in symmetric random environment
- Central limit theorem for additive functionals of reversible Markov processes and applications to simple exclusions
- Upper bounds for symmetric Markov transition functions
- A new proof of Moser's parabolic Harnack inequality using the old ideas of Nash
- Density and uniqueness in percolation
- Weak convergence of a random walk in a random environment
- Parabolic Harnack inequality and estimates of Markov chains on graphs
- A lower bound on the variance of conductance in random resistor networks
- Random walk on the infinite cluster of the percolation model
- Heat kernel upper bounds on a complete non-compact manifold
- Domination by product measures
- Motion by mean curvature from the Ginzburg-Landau \(\nabla\phi\) interface model
- Approximation of the effective conductivity of ergodic media by periodization
- 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
- Bulk transport properties and exponent inequalities for random resistor and flow networks
- The central limit theorem for Markov chains started at a point
- Equilibrium fluctuations for \(\nabla\varphi\) interface model
- Central limit theorems for additive functionals of Markov chains.
- Finite volume approximation of the effective diffusion matrix: The case of independent bond disorder
- Isoperimetry and heat kernel decay on percolation clusters.
- Quenched invariance principles for walks on clusters of percolation or among random conduc\-tances
- Biased random walks on Galton-Watson trees
- Trapping in the random conductance model
- Martingale approximation and optimality of some conditions for the central limit theorem
- Heat-kernel estimates for random walk among random conductances with heavy tail
- Invariance principle for the random conductance model with unbounded conductances
- On homogenization and scaling limit of some gradient perturbations of a massless free field
- On the exactness of the Wu-Woodroofe approximation
- A quenched invariance principle for non-elliptic random walk in i.i.d. balanced random environment
- Functional CLT for random walk among bounded random conductances
- A central limit theorem for biased random walks on Galton-Watson trees
- Quenched invariance principles for random walks with random conductances
- Extremes of the discrete two-dimensional Gaussian free field
- Some aspects of recent works on limit theorems in ergodic theory with special emphasis on the ``central limit theorem
- Evolving sets, mixing and heat kernel bounds
- On estimating the derivatives of symmetric diffusions in stationary random environment, with applications to \(\nabla\varphi\) interface model
- Phase coexistence of gradient Gibbs states
- Gaussian free fields for mathematicians
- Faster mixing via average conductance
- A conditional quenched CLT for random walks among random conductances on $\mathbb{Z}^d$
- First-passage percolation, network flows and electrical resistances
- Subdiffusive heat-kernel decay in four-dimensional i.i.d. random conductance models
- Bounds on the L 2 Spectrum for Markov Chains and Markov Processes: A Generalization of Cheeger's Inequality
- Continuity of Solutions of Parabolic and Elliptic Equations
- The supercritical phase of percolation is well behaved
- Sur le nombre de points visités par une marche aléatoire sur un amas infini de percolation
- Diffusion of color in the simple exclusion process
- Percolation
- Large Deviations for Heat Kernels on Graphs