Asaf Nachmias

We study the probability that the origin is connected to the sphere of radius R in critical percolation in high dimensions, namely when the dimension d is a large fixed constant, or when d>6 and the lattice is sufficiently spread out. I will present...

We show that the electric resistance between the origin and the n-th generation of a critical oriented branching random walk in dimensions d6 is at most n^(1-a) for some a>0. As a corollary, the spectral dimension of the trace is strictly larger...

I will describe two results concerning random walks on planar graphs and the connections with Koebe's circle packing theorem (which I will not assume any knowledge of):1. A bounded degree planar triangulation is recurrent if and only if the set of...