Table of contents
About this book
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.
- Book Title Random Walks in the Quarter Plane
- Book Subtitle Algebraic Methods, Boundary Value Problems, Applications to Queueing Systems and Analytic Combinatorics
- Series Title Probability Theory and Stochastic Modelling
- Series Abbreviated Title Probability and Stochastic (formerly: PIA & SMAP)
- DOI https://doi.org/10.1007/978-3-319-50930-3
- Copyright Information Springer International Publishing AG 2017
- Publisher Name Springer, Cham
- eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
- Hardcover ISBN 978-3-319-50928-0
- Softcover ISBN 978-3-319-84525-8
- eBook ISBN 978-3-319-50930-3
- Series ISSN 2199-3130
- Series E-ISSN 2199-3149
- Edition Number 2
- Number of Pages XVII, 248
- Number of Illustrations 17 b/w illustrations, 0 illustrations in colour
- Additional Information Originally published with the subtitle: Algebraic Methods, Boundary Value Problems and Applications
Probability Theory and Stochastic Processes
Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences
Probability and Statistics in Computer Science
Difference and Functional Equations
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