Invariance principle for the random conductance model in a degenerate ergodic environment
By S. Andres, Jean-Dominique Deuschel, Martin Slowik. 2013
84 citations recorded by the source corpus.
We study a continuous time random walk, X, on Zd in an environment of random conductances taking values in (0,∞). We assume that the law of the conductances is ergodic with respect to space shifts. We prove a quenched invariance principle for X under some moment conditions of the environment. The key result on the sublinearity of the corrector is obtained by Moser’s iteration scheme.
Subfields: Finance, Mathematical Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/2c2cb5870271bad54aae3d9f46586f194c4b9a55
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Finance
In Mathematical Physics
In Statistical and Nonlinear Physics
Citations in the corpus
- Local Boundedness and Harnack Inequality for Solutions of Linear Nonuniformly Elliptic Equations (2019, background): “stichomogenizationfor uniformly elliptic equations dates back to the classical papers [28, 22]. Currently, stochastic homogenization beyond uniform ellipticity is an active field of research, see e.g. [1, 2, 3, 4, 6, 10, 13, 17, 18, 27]. A central object in the homogenization of linear elliptic equat”
- Harnack inequalities on weighted graphs and some applications to the random conductance model (2013, methodology): “Since |x|/n ≤ 1 and h(t) ∈ [1, 4] for t ≥ 1 we have c−1 ≤ kh(t)(x/n) ≤ c for some c > 0 independent of t, x and n.”
- Quenched invariance principle for random walks with time-dependent ergodic degenerate weights (2016, methodology): “We follow the argument in proof of [10], Lemma 2 (cf. also [3], Proposition 2.9).”