Three-Point Markov Extension and an Improved Upper Bound for Survival Probability of the One-Dimensional Contact Process

抄録

The survival probability σ(A) is studied for the one-dimensional contact process. An approximate function h⁽³⁾(A) for σ(A) is obtained; a partial stationary condition is used to determine h⁽³⁾(C_i) for small sets C_i’s and then it is extended to all finite subsets A of Z¹ by the Markov extension. It is proved that h⁽³⁾(A) gives an upper bound for σ(A) in the parameter region where the infection rate λ is greater than Griffeath’s lower bound for λ_c, i.e. (Remark: Graphics omitted.). The present result improves previous upper bounds.