Abstract:

In this article, we discuss several properties of the basic contact process on hexagonal lattice ${\Bbb H}$, showing that it behaves quite similar to the process on d-dimensional lattice Z^d in many aspects. Firstly, we construct a coupling between the contact process on hexagonal lattice and the oriented percolation, and prove an equivalent finite space-time condition for the survival of the process. Secondly, we show the complete convergence theorem and the polynomial growth hold for the contact process on hexagonal lattice. Finally, we prove exponential bounds in the supercritical case and exponential decay rates in the subcritical case of the process.

Key words: Hexagonal lattice, contact process, critical value, complete convergence theorem, rate of growth