Random Walks in the Quarter Plane: Algebraic Methods, Boundary Value Problems, Applications to Queueing Systems and Analytic Combinatorics - Archive ouverte HAL Access content directly
Books Year : 2017

Random Walks in the Quarter Plane: Algebraic Methods, Boundary Value Problems, Applications to Queueing Systems and Analytic Combinatorics

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Abstract

This monograph aims to promote original mathematical methods to determine the invari- ant measure of two-dimensional random walks in domains with boundaries. Such processes are encountered in numerous applications and are of interest in several areas of mathemat- ical research like Stochastic Networks, Analytic Combinatorics, Quantum Physics. This second edition consists of two parts. Part I is a revised upgrade of the rst edition (1999), with additional recent results on the group of the random walk. The theoretical approach given therein has been developed by the authors since the early 1970s. By using Complex Function Theory, Boundary Value Problems, Riemann Surfaces, Galois Theory, completely new methods are proposed for solving functional equations of two complex variables, which can also be applied to characterize the Transient Behavior of the walks, as well as to nd explicit solution to the one-dimensional Quantum Three-Body Problem, or to tackle a new class of Integrable Systems. Part II borrows speci c case-studies from queueing theory (in particular the famous problem of Joining the Shorter of Two Queues), and enumerative combinatorics (Counting, Asymptotics).

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hal-01651919 , version 1 (29-11-2017)

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Guy Fayolle, Roudolf Iasnogorodski, Vadim A. Malyshev. Random Walks in the Quarter Plane: Algebraic Methods, Boundary Value Problems, Applications to Queueing Systems and Analytic Combinatorics. Soren Asmussen; Peter W. Glynn; Yves Le Jan. Springer International Publishing, 40, pp.255, 2017, Probability Theory and Stochastic Modelling, Peter W. Glynn, Stanford, CA, USA, 978-3-319-50928-0. ⟨10.1007/978-3-319-50930-3⟩. ⟨hal-01651919⟩
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