INHOMOGENEOUS APPROXIMATION OF THE CRITICAL NEAREST PARTICLE-SYSTEMS

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:48

Article

关键词: INFINITE PARTICLE SYSTEMS;    NEAREST PARTICLE SYSTEMS;    SURVIVAL;    EXTINCTION;   

DOI  :  10.1016/0304-4149(93)90047-8

来源: Elsevier

【 摘 要 】

In this paper we consider reversible nearest particle systems defined by lambda(x) = 1 + f(x) and beta(n) = c(alpha)n(-alpha), alpha > 1. When alpha > 2, let f(x) = - b/(b + Absolute value of x gamma), b > 0. Let m be the first moment of beta(n). Then the system survives if gamma > 1 or gamma = 1 and alpha > 2 (1 + b/m) and dies out if gamma < 1 and alpha < 2(1 + b/m). When 1 < alpha less-than-or-equal-to 2, let f(x) = b/(1 + Absolute value of x gamma), b > 0, gamma > 0. Then the system survives if gamma > alpha - 1 or gamma < alpha - 1 and b > b(c) and dies out if gamma < alpha-1 or gamma = alpha - 1 and b < b(> c) where b(c) is ome positive finite constant.

【 授权许可】

Free