Logarithmic correction to resistance

Abstract

We study the trace of the incipient infinite oriented branching random walk in ${\mathbb{Z}}^d\times {\mathbb{Z}}_{+}$ when the dimension is $d=6$. Under suitable moment assumptions, we show that the electrical resistance between the root and level $n$ is $O(n{\log }^{-\xi }n)$ for a $\xi >0$ that does not depend on details of the model.

45 pages, 6 figures - Minor changes made to take into account the referee's comments