In this article, the authors mainly discuss the law of large number under Kalikow＇s condition for multi-dimensional random walks in random environment with holding times. The authors give an expression to the escape speed of random walks in terms of the Lyapounov exponents, which have been precisely used in the context of large deviation.
We investigate the contact process on random graphs generated from the configuration model for scale-free complex networks with the power law exponent β E （2, 3]. Using the neighborhood expansion method, we show that, with positive probability, any disease with an infection rate λ 〉 0 can survive for exponential time in the number of vertices of the graph. This strongly supports the view that stochastic scale-free networks are remarkably different from traditional regular graphs, such as, Z^d and classical Erdos-Renyi random graphs.
Techniques of Burton-Keane,developed earlier for independent percolation on Zd,are adapted to the setting of locally dependent percolation on Zd for d 2.The main result of this paper is a uniqueness theorem,that there exists almost surely a unique infinite out-cluster in locally dependent percolation on Zd,under the finite energy condition.
