On symmetric random walks with random conductances on ℤd

By L. Fontes, Pierre Mathieu. 2004

47 citations recorded by the source corpus.

We study models of continuous time, symmetric, ℤd-valued random walks in random environments. One of our aims is to derive estimates on the decay of transition probabilities in a case where a uniform ellipticity assumption is absent. We consider the case of independent conductances with a polynomial tail near 0 and obtain precise asymptotics for the annealed return probability and convergence times for the random walk confined to a finite box.

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

View Paper: https://www.semanticscholar.org/paper/a20c9ae6b08d71aea4a2e60f584e64ddf1cc0a16

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In Condensed Matter Physics

In Mathematical Physics

In Statistics and Probability

Citations in the corpus

Harnack inequalities on weighted graphs and some applications to the random conductance model (2013, background): “While for the example in [23], where the conductances are given by ω(x, y) = θω(x) ∧ θω(y) for a family {θω(x) : x ∈ Zd} of”
Recent progress on the Random Conductance Model (2011, methodology): “istribution with these properties, the isoperimetry methods sketched above yield a vacuous conclusion. The situation becomes even more suspicious after an inspection of the work of Fontes and Mathieu [59] in which they design a family of models — not with i.i.d. conductances but close enough — in wh”
Processes on Unimodular Random Networks (2006, background): “We illustrate this by extending results of Pittet and Saloff-Coste (2000) and Fontes and Mathieu (2006) on return probabilities of continuous-time random walks.”
Variance decay for functionals of the environment viewed by the particle (2009, background): “(3) The previous results no longer hold (even qualitatively) without the assumption that the jump rates are bounded away from 0. We refer to [ FM06 ] or [BBHK08] for evidence of the anomalous behaviour of the return probabilities in this case.”