{"product_id":"random-walks-in-the-quarter-plane-algebraic-methods-boundary-value-problems-applications-to-queueing-systems-and-analytic-combinatorics-9783319845258","title":"Random Walks in the Quarter Plane: Algebraic Methods, Boundary Value Problems, Applications to Queueing Systems and Analytic Combinatorics","description":"\u003cp\u003e • Author(s): Guy Fayolle\u003cbr\u003e • Publisher: Springer\u003cbr\u003e • Publisher Imprint: Springer\u003cbr\u003e • BISAC: Probability \u0026amp; Statistics - General\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003cb\u003eFrom the Back Cover\u003c\/b\u003e\u003cbr\u003e\u003c\/p\u003e\u003cp\u003eThis 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 \u003ci\u003eStochastic Networks\u003c\/i\u003e, \u003ci\u003eAnalytic Combinatorics\u003c\/i\u003e, and \u003ci\u003eQuantum Physics\u003c\/i\u003e. This second edition consists of two parts.\u003c\/p\u003e\u003cp\u003ePart 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 \u003ci\u003eComplex Function Theory\u003c\/i\u003e, \u003ci\u003eBoundary\u003c\/i\u003e \u003ci\u003eValue Problems\u003c\/i\u003e, \u003ci\u003eRiemann Surfaces\u003c\/i\u003e, and \u003ci\u003eGalois Theory\u003c\/i\u003e, completely new methods are proposed for solving functional equations of two complex variables, which can also be applied to characterize the \u003ci\u003eTransient Behavior\u003c\/i\u003e of the walks, as well as to find explicit solutions to the one-dimensional \u003ci\u003eQuantum Three-Body Problem\u003c\/i\u003e, or to tackle a new class of Integrable Systems.\u003c\/p\u003e\u003cp\u003e\u003cb\u003ePart II\u003c\/b\u003e borrows special case-studies from queueing theory (in particular, the famous problem of \u003ci\u003eJoining the Shorter of Two Queues\u003c\/i\u003e) and enumerative combinatorics (\u003ci\u003eCounting\u003c\/i\u003e, \u003ci\u003eAsymptotics\u003c\/i\u003e).\u003c\/p\u003e\u003cp\u003eResearchers and graduate students should find this book very useful.\u003c\/p\u003e","brand":"Springer","offers":[{"title":"Paperback","offer_id":45276861989015,"sku":"9783319845258","price":7277.0,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0666\/3471\/1191\/files\/9783319845258.webp?v=1769286857","url":"https:\/\/atlanticbooks.com\/products\/random-walks-in-the-quarter-plane-algebraic-methods-boundary-value-problems-applications-to-queueing-systems-and-analytic-combinatorics-9783319845258","provider":"Atlantic Books","version":"1.0","type":"link"}