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In this paper we are concerned with the contact process on the squaredlattice. The contact process intuitively describes the spread of the infectiousdisease on a graph, where an infectious vertex becomes healthy at a constantrate while a healthy vertex is infected at rate proportional to the number ofinfectious neighbors. As the dimension of the lattice grows to infinity, wegive a mean field limit for the survival probability of the process conditionedon the event that only the origin of the lattice is infected at t=0. The binarycontact path process is a main auxiliary tool for our proof.

Mean field limit for survival probability of the high-dimensional contact process