Random Walks in the Quarter Plane (2nd ed.)

This monograph aims to promote original mathematical methods to determine the invariant measure of two-dimensional random walks in domains with boundaries. Such processes arise in numerous applications and are of interest in several areas of mathematical research, such as Stochastic Networks , Analytic Combinatorics , and Quantum Physics . This second edition consists of two parts. Part I is a revised upgrade of the first edition (1999), with additional recent results on the group of a rand