Absence of mutual unbounded growth for almost all parameter values in the two-type Richardson model

We study the two-type Richardson model on Zd, d⩾2, in the asymmetric case where the two particle types have different infection rates. Starting with a single particle of each type, and fixing the infection rate for one of the types, we show that mutual unbounded growth has probability 0 for all but at most countably many values of the other typeʹs infection rate.