Filling the Hypercube in the Supercritical Contact Process in Equilibrium
1998, v.4, №1, 113-130
We consider the supercritical d-dimensional contact process, obtaining new results on the asymptotic distribution of the first occurrence time of an anomalous density of particles in a fixed region of the space, when the process starts from equilibrium. In particular, we get uniform sharp bounds for the rates of convergence in distribution to a mean 1 exponential random variable, when suitably rescaled, of the first time for which the hypercube is totally occupied.
Keywords: contact process,occurrence time of a rare event,large deviations,infinite particle system