Random Walks in the Quarter Plane Algebraic Methods Boundary Value Problems Applications to Queueing Systems and Analytic Combinatorics 2nd Edition by Guy Fayolle, Roudolf Iasnogorodski, Vadim Malyshev ISBN 331984525X 978-3319845258

Random Walks in the Quarter Plane Algebraic Methods Boundary Value Problems Applications to Queueing Systems and Analytic Combinatorics 2nd Edition by Guy Fayolle, Roudolf Iasnogorodski, Vadim Malyshev- Ebook PDF Instant Download/Delivery: 331984525X, 978-3319845258

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Product details:

ISBN 10: 331984525X 

ISBN 13: 978-3319845258

Author: Guy Fayolle, Roudolf Iasnogorodski, Vadim Malyshev

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.

Table of contents: 

Chapter 1: Probabilistic Background
Chapter 2: Foundations of the Analytic Approach
Chapter 3: Analytic Continuation of the Unknown Functions in the Genus 1 Case
Chapter 4: The Case of a Finite Group
Chapter 5: Solution in the Case of an Arbitrary Group
Chapter 6: The Genus 0 Case
Chapter 7: Criterion for the Finiteness of the Group in the Genus 0 Case
Chapter 8: Miscellanea
Chapter 9: A Two-Coupled Processor Model
Chapter 10: Joining the Shorter of Two Queues: Reduction to a Generalized BVP
Chapter 11: Counting Lattice Walks in the Quarter Plane
Chapter 12: Correction to: Random Walks in the Quarter Plane

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Tags: Guy Fayolle, Roudolf Iasnogorodski, Vadim Malyshev, Random Walks, Quarter Plane, Algebraic Methods, Boundary Value Problems, Queueing Systems, Analytic Combinatorics