Random Walks in the Quarter Plane : Algebraic Methods, Boundary Value Problems, Applications to Queueing Systems and Analytic Combinatorics
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The work Random Walks in the Quarter Plane : Algebraic Methods, Boundary Value Problems, Applications to Queueing Systems and Analytic Combinatorics represents a distinct intellectual or artistic creation found in European University Institute. This resource is a combination of several types including: Work, Language Material, Books.
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Random Walks in the Quarter Plane : Algebraic Methods, Boundary Value Problems, Applications to Queueing Systems and Analytic Combinatorics
Resource Information
The work Random Walks in the Quarter Plane : Algebraic Methods, Boundary Value Problems, Applications to Queueing Systems and Analytic Combinatorics represents a distinct intellectual or artistic creation found in European University Institute. This resource is a combination of several types including: Work, Language Material, Books.
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 Random Walks in the Quarter Plane : Algebraic Methods, Boundary Value Problems, Applications to Queueing Systems and Analytic Combinatorics
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 Algebraic Methods, Boundary Value Problems, Applications to Queueing Systems and Analytic Combinatorics
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 by Guy Fayolle, Roudolf Iasnogorodski, Vadim Malyshev
 Language
 eng
 Summary
 This monograph aims to promote original mathematical methods to determine the invariant measure of twodimensional 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 onedimensional Quantum ThreeBody Problem, or to tackle a new class of Integrable Systems. Part II borrows special casestudies 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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 Springer eBooks
 Probability Theory and Stochastic Modelling,
 Series volume
 40
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