Probability Seminar: Asaf Nachmias

We show that the electric resistance between the origin and the n-th generation of a critical oriented branching random walk in dimensions d<6 is at most n^(1-a) for some a>0. As a corollary, the spectral dimension of the trace is strictly larger than 4/3 (its value when d>6) answering a question of Barlow, Jarai , Kumagai and Slade.

Joint work with Antal Jarai.