This book is devoted exclusively to a very special class of random processes, namely to random walk on the lattice points of ordinary Euclidean space. The author considered this high degree of specialization worth while, because of the theory of such random walks is far more complete than that of any larger class of Markov chains. The book will present no technical difficulties to the readers with some solid experience in analysis in two or three of the following areas: probability theory, real… Expand

This text meets the need for a modern reference to the detailed properties of an important class of random walks on the integer lattice and is suitable for probabilists, mathematicians working in related fields, and for researchers in other disciplines who use random walks in modeling.Expand

This paper concerns random walks on periodic graphs embedded in the d-dimensional Euclidian space R d and obtains asymptotic expansions of the Green functions of them up to the second order term,… Expand

We study the asymptotic behaviour of the probability that a weighted sum of centered i.i.d. random variables Xk does not exceed a constant barrier. For regular random walks, the results follow easily… Expand

The purpose of this paper is to review results concerning the behaviour at inifinity of random walks on graphs and (as a special case) groups and closely related questions concerning the associated… Expand

Limit theorems are proved for the range of d-dimensional random walks in the domain of attraction of a stable process of index P3. The range Rn is the number of distinct sites of Zd visited by the… Expand

In this course we follow recent advances in the study of the fractal nature of certain random sets, emphasizing the methods used to obtain such results. We focus on some of the fine properties of the… Expand