Inhomogeneous approximation of the critical nearest particle systems

Xijian Liu

Stochastic Processes and their Applications, 1993, vol. 48, issue 2, 251-275

Abstract: 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 + 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] 0, [gamma] > 0. Then the system survives if [gamma] > [alpha] - 1 or [gamma] bc and dies out if [gamma] c where bc is ome positive finite constant.

Keywords: infinite; particle; systems; nearest; particle; systems; survival; extinction (search for similar items in EconPapers)
Date: 1993
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