Advertisement

© 2017

Random Walks in the Quarter Plane

Algebraic Methods, Boundary Value Problems, Applications to Queueing Systems and Analytic Combinatorics

Book

Part of the Probability Theory and Stochastic Modelling book series (PTSM, volume 40)

Table of contents

  1. Front Matter
    Pages i-xvii
  2. The General Theory

    1. Front Matter
      Pages 1-1
    2. Guy Fayolle, Roudolf Iasnogorodski, Vadim Malyshev
      Pages 3-8
    3. Guy Fayolle, Roudolf Iasnogorodski, Vadim Malyshev
      Pages 9-35
    4. Guy Fayolle, Roudolf Iasnogorodski, Vadim Malyshev
      Pages 37-53
    5. Guy Fayolle, Roudolf Iasnogorodski, Vadim Malyshev
      Pages 55-117
    6. Guy Fayolle, Roudolf Iasnogorodski, Vadim Malyshev
      Pages 119-154
    7. Guy Fayolle, Roudolf Iasnogorodski, Vadim Malyshev
      Pages 155-170
    8. Guy Fayolle, Roudolf Iasnogorodski, Vadim Malyshev
      Pages 171-182
    9. Guy Fayolle, Roudolf Iasnogorodski, Vadim Malyshev
      Pages 183-191
  3. Applications to Queueing Systems and Analytic Combinatorics

    1. Front Matter
      Pages 193-193
    2. Guy Fayolle, Roudolf Iasnogorodski, Vadim Malyshev
      Pages 195-200
    3. Guy Fayolle, Roudolf Iasnogorodski, Vadim Malyshev
      Pages 201-219
    4. Guy Fayolle, Roudolf Iasnogorodski, Vadim Malyshev
      Pages 221-241
  4. Back Matter
    Pages 243-248

About this book

Introduction

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 NetworksAnalytic 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 TheoryBoundary Value ProblemsRiemann 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 (CountingAsymptotics).

Researchers and graduate students should find this book very useful.

Keywords

60G50, 39B32, 32A26, 30D05, 46N50 algebraic methods analytic combinatorics boundary value problems functional equations random walks in the quarter plane

Authors and affiliations

  1. 1.INRIA Paris-­‐RocquencourtLe ChesnayFrance
  2. 2.ParisFrance
  3. 3.Faculty of Mechanics and MathematicsMoscow Lomonosov State UniversityMoscowRussia

About the authors

G. FAYOLLE: Engineer degree from École Centrale in 1967, Doctor-es-Sciences (Mathematics) from University of Paris 6, 1979. He joined INRIA in 1971. Research Director and team leader (1975-2008), now Emeritus. He has written about 100 papers in Analysis, Probability and Statistical Physics.

R. IASNOGORODSKI: Doctor-es-Sciences (Mathematics) from University of Paris 6, 1979. Associate Professor in the Department of Mathematics at the University of Orléans (France), 1977-2003. He has written about 30 papers in Analysis and Probability.

V.A. MALYSHEV: 1955-1961 student Moscow State University, 1967-nowadays Professor at Moscow State University, 1990-2005 Research Director at INRIA (France). He has written about 200 papers in Analysis, Probability and Mathematical Physics.

Bibliographic information

Industry Sectors
Pharma
Biotechnology
IT & Software
Telecommunications
Finance, Business & Banking
Electronics
Energy, Utilities & Environment
Aerospace
Oil, Gas & Geosciences
Engineering