Quenched invariance principles for random walks on percolation clusters

By Pierre Mathieu, Andrey L. Piatnitski. Proceedings of the Royal Society A, 2005

211 citations recorded by the source corpus.

We consider a supercritical Bernoulli percolation model in , d≥2, and study the simple symmetric random walk on the infinite percolation cluster. The aim of this paper is to prove the almost sure (quenched) invariance principle for this random walk.

Subfields: Condensed Matter Physics, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/7bfee657d3646344e638bed7ade846eb81c0104a

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Condensed Matter Physics

In Mathematical Physics

In Statistics and Probability

Citations in the corpus

Recent progress on the Random Conductance Model (2011, methodology): “A construction along the above lines can be found in the paper of Mathieu and Piatnitski [101] for the problem of supercritical percolation cluster and in Biskup and Prescott [18] at the current level of generality.”
The Alexander-Orbach conjecture holds in high dimensions (2008, background): “In particular, the random walk on the supercritical infinite cluster has an invariance principle, the spectral dimension is ds = d and other Z d-like properties hold, see [19, 13, 5, 49, 15, 42].”
Quenched invariance principle for random walks with time-dependent ergodic degenerate weights (2016, unknown): “The proof is based on the martingale convergence theorem by Helland (see Theorem 5.1(a) in [22]); the proofs in [2] or [30] can be easily transferred into the time dynamic setting.”
Quenched invariance principle for random walks in balanced random environment (2010, background): “Much of this work has been in the context of reversible models, either for walks on percolation clusters or for the random conductance model, see [1, 19, 15, 4, 16, 14, 2].”
Invariance principle for the random conductance model in a degenerate ergodic environment (2013, methodology): “Following [31], we introduce an orthogonal decomposition of the space L(2)cov.”