Electrical resistance of the low dimensional critical branching random walk

We show that the electric resistance between the origin and the n-th generation of a critical oriented branching random walk trace in dimensions d < 6 is at most O(n^{1-alpha}) for some universal alpha > 0. As a corollary, the mean exit time of the simple random walk on the trace from a ball in the graph distance is polynomially smaller than in d > 6, answering a question of Barlow, Jarai, Kumagai and Slade. (Joint work with Asaf Nachmias)