Source： ENG
Place of Publication： Europe
Academic Level： Graduate
Book Data Full Description：
This introduction to random walks focuses on simpler aspects of the subject such as Markovian models or models closely related to a Markovian formulation. Emphasis is placed on asymptotic properties of random walks, and an introductory account of Abelian and Taubernian theorems is also included. Both the formalism and many of the attendant ideas related to the random walk lie at the core of a significant fraction of contemporary research in statistical physics. In the language of physics the random walk can be described as a microscopic model for transport processes which have some element of randomness. The starting point of nearly all analyses of transport in disordered media is to be found in one or another type of random walk model. Mathematical formalism based on the theory of random walks is not only pervasive in a number of areas of physics, but also finds application in many areas of chemistry. The random walk has also been applied to the study of a number of biological phenomena. This book provides an introduction to the subject which should be of interest to students and more senior researchers who have had no prior contact with the field; the author has focused on simpler aspects of the subject, mainly on Markovian models, or models closely related to a Markovian formulation. Such models are exemplified by the continuous-time random walk which has both Markovian and non-Markovian aspects. Considerable emphasis has been placed on asymptotic properties of random walks because their universal properties are the ones that permit such a wide range of applications of the mathematical formalism. Attention is also given to an introductory account of Abelian and Tauberian theorems.(Contents List) Introductory comments; the ubiquitous characteristic function; asymptotic properties and the diffusion limit; lattice walks; boundaries and constraints; multistate random walks; selected applications.
