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Martin Barlow

Publications and source records attributed to Martin Barlow.

4 recordsLinked to original sources
arXiv2013

Comparison of quenched and annealed invariance principles for random conductance model: Part II

We show that there exists an ergodic conductance environment such that the weak (annealed) invariance principle holds for the corresponding continuous time random walk but the quenched invariance principle does not hold. In the present paper we give a proof of the full scaling limit for the weak invariance principle, improving the result in an earlier paper where we obtained a subsequential limit.

math.PR↗
arXiv2008

Parabolic Harnack Inequality and Local Limit Theorem for Percolation Clusters

We consider the random walk on supercritical percolation clusters in the d-dimensional Euclidean lattice. Previous papers have obtained Gaussian heat kernel bounds, and a.s. invariance principles for this process. We show how this information leads to a parabolic Harnack inequality, a local limit theorem and estimates on the Green's function.

math.PR↗
arXiv1999

Coalescence of skew Brownian motions

We prove that two skew Brownian motions with the same skewness parameter (different from 0) and driven by the same Brownian motion coalesce a.s.

math.PR↗