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Titlebook: Random Walks in the Quarter Plane; Algebraic Methods, B Guy Fayolle,Roudolf Iasnogorodski,Vadim Malyshev Book 2017Latest edition Springer I

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发表于 2025-3-21 19:16:08 | 显示全部楼层 |阅读模式
书目名称Random Walks in the Quarter Plane
副标题Algebraic Methods, B
编辑Guy Fayolle,Roudolf Iasnogorodski,Vadim Malyshev
视频videohttp://file.papertrans.cn/822/821099/821099.mp4
概述Promotes original analytic methods to determine the invariant measure of two-dimensional random walks in domains with boundaries. These processes appear in several mathematical areas (Stochastic Netwo
丛书名称Probability Theory and Stochastic Modelling
图书封面Titlebook: Random Walks in the Quarter Plane; Algebraic Methods, B Guy Fayolle,Roudolf Iasnogorodski,Vadim Malyshev Book 2017Latest edition Springer I
描述.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 (.Counti
出版日期Book 2017Latest edition
关键词60G50, 39B32, 32A26, 30D05, 46N50; algebraic methods; analytic combinatorics; boundary value problems; f
版次2
doihttps://doi.org/10.1007/978-3-319-50930-3
isbn_softcover978-3-319-84525-8
isbn_ebook978-3-319-50930-3Series ISSN 2199-3130 Series E-ISSN 2199-3149
issn_series 2199-3130
copyrightSpringer International Publishing AG 2017
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发表于 2025-3-21 21:16:07 | 显示全部楼层
Foundations of the Analytic ApproachThis chapter presents the essential stepping stones of the analytic approach. They require in particular some basic notions concerning Riemann surfaces and algebraic curves.
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发表于 2025-3-22 04:27:15 | 显示全部楼层
The Case of a Finite GroupIn Sect. ., the group . of the random walk was shown to be of even order ..
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发表于 2025-3-22 11:59:33 | 显示全部楼层
Criterion for the Finiteness of the Group in the Genus 0 CaseThe goal of this chapter is to derive a concrete necessary and sufficient condition for the finiteness of . (the group of the random walk introduced in Definition .) in the genus 0 case.
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发表于 2025-3-22 15:25:19 | 显示全部楼层
MiscellaneaIn the first 7 chapters, we fully described only some of the topics related to the subject. There are, however, many directly related questions which, although not dealt with in the present book, deserve mention in this chapter so as to provide a panoramic overview.
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发表于 2025-3-23 00:04:23 | 显示全部楼层
Counting Lattice Walks in the Quarter PlaneEnumeration of planar lattice walks has become a classical topic in combinatorics. For a given set . of allowed jumps (or steps), it is a matter of counting the number of paths starting from some point and ending at some arbitrary point in a given time, and possibly restricted to some regions of the plane.
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发表于 2025-3-23 08:29:14 | 显示全部楼层
Guy Fayolle,Roudolf Iasnogorodski,Vadim MalyshevPromotes original analytic methods to determine the invariant measure of two-dimensional random walks in domains with boundaries. These processes appear in several mathematical areas (Stochastic Netwo
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