THE THRESHOLD VOTER AUTOMATON AT A CRITICAL-POINT

We consider the threshold voter automaton in one dimension with thresh old tau > n/2, where n is the number of neighbors and where we start f rom a product measure with density 1/2. It has recently been shown tha t there is a critical value theta(c) approximate to 0.6469076, so that if tau = theta n with theta > theta(c) and n is large, then most site s never flip, while for theta epsilon (1/2, theta(c)) and n large, the re is a limiting state consisting mostly of large regions of points of the same type. Using a supercritical branching process, we show that the behavior at theta(c) differs from both the theta > theta(c) regime and the theta < theta(c) regime and that, in some sense, there is a d iscontinuity both from the left and from the right at this critical va lue.