215 citations · 217 across the 4 of their papers we have counts for
5 papers · 1 filter
Random walk on the incipient infinite cluster on trees
Martin T. Barlow, Takashi Kumagai
Let be the incipient infinite cluster (IIC) for percolation on a homogeneous tree of degree . We obtain estimates for the transition density of the continuous tim…
Diffusion limited aggregation on a tree
MArtin T. Barlow, Robin Pemantle, Edwin A. Perkins
We study the following growth model on a regular d-ary tree. Points at distance n adjacent to the existing subtree are added with probabilities proportional to alpha^{-n}, where al…
Some remarks on the elliptic Harnack inequality
Martin T. Barlow
This note gives three short results concerning the elliptic Harnack inequality (EHI), in the context of random walks on graphs. The first is that the EHI implies polynomial growth…
Random walks on supercritical percolation clusters
Martin T. Barlow
We obtain Gaussian upper and lower bounds on the transition density q_t(x,y) of the continuous time simple random walk on a supercritical percolation cluster C_{\infty} in the Eucl…
Coalescence of skew Brownian motions
Martin Barlow, Krzysztof Burdzy, Haya Kaspi +1
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.