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## Details

Genre/Form: | Electronic books |
---|---|

Additional Physical Format: | Print version: Fayolle, G. (Guy), 1943- Random Walks in the Quarter-plane. Cham, Switzerland : Springer Nature, [2017] (OCoLC)963914166 |

Material Type: | Document, Internet resource |

Document Type: | Internet Resource, Computer File |

All Authors / Contributors: |
G Fayolle; Roudolf Iasnogorodski; V A Malyshev |

ISBN: | 9783319509303 3319509306 |

OCLC Number: | 971613451 |

Description: | 1 online resource. |

Contents: | Part 1. The General Theory. Probabilistic Background ; Foundations of the Analytic Approach ; Analytic Continuation of the Unknown Functions in the Genus 1 Case ; The Case of a Finite Group ; Solution in the Case of an Arbitrary Group ; The Genus 0 Case ; Criterion for the Finiteness of the Group in the Genus 0 Case ; Miscellanea -- part 2. Applications to Queueing Systems and Analytic Combinatorics. A Two-Coupled Processor Model ; Joining the Shorter of the Two Queues: Reduction to a Generalized BVP ; Counting Lattice Walks in the Quarter Plane. |

Series Title: | Probability theory and stochastic modelling, v. 40. |

Responsibility: | Guy Fayolle, Roudolf Iasnogorodski, Vadim Malyshev. |

### Abstract:

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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