  The goal of this work is to find the asymptotics of the hitting probability
of a distant point for the voter model on the integer lattice started from a
single 1 at the origin. In dimensions 2 or 3, we obtain the precise asymptotic
behavior of this probability. We use the scaling limit of the voter model
started from a single 1 at the origin in terms of super-Brownian motion under
its excursion measure. This invariance principle was stated by Bramson, Cox and
Le Gall, as a consequence of a theorem of Cox, Durrett and Perkins. Less
precise estimates are derived in dimensions greater than 4.
