Random Walks in the Quarter Plane : Algebraic Methods, Boundary Value Problems, Applications to Queueing Systems and Analytic Combinatorics
Softcover reprint of the original 2nd ed. 2017
Book Details
Format
Paperback / Softback
Book Series
Probability Theory and Stochastic Modelling
ISBN-10
331984525X
ISBN-13
9783319845258
Edition
Softcover reprint of the original 2nd ed. 2017
Publisher
Springer International Publishing AG
Imprint
Springer International Publishing AG
Country of Manufacture
GB
Country of Publication
GB
Publication Date
Jul 13th, 2018
Print length
248 Pages
Ksh 16,200.00
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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 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, and 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 find explicit solutions to the one-dimensional Quantum Three-Body Problem, or to tackle a new class of Integrable Systems. Part II borrows special case-studies from queueing theory (in particular, the famous problem of Joining the Shorter of Two Queues) and enumerative combinatorics (Counting, Asymptotics). Researchers and graduate students should find this book very useful.
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