{"product_id":"331984525x","title":"Random Walks in the Quarter Plane: Algebraic Methods","description":"\u003cp\u003eIn this review of Random Walks in the Quarter Plane the reviewer finds a mathematically rigorous monograph aimed at researchers and advanced graduate students interested in two-dimensional stochastic processes. The single biggest reason to consider this book is its systematic presentation of original algebraic and complex-analytic methods that address the invariant measure for random walks with boundaries; the text emphasizes theoretical tools developed over decades and presents them in a form useful to specialists working in \u003cstrong\u003estochastic networks\u003c\/strong\u003e and analytic combinatorics.\u003c\/p\u003e\n\u003ch2\u003eKey Features\u003c\/h2\u003e\n\u003cul\u003e\n\u003cli\u003e\n\u003cstrong\u003eComprehensive theoretical approach:\u003c\/strong\u003e The book collects a long-running research program combining Complex Function Theory and Boundary Value Problems, offering readers a unified set of methods for two-variable functional equations.\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003eUpdated edition:\u003c\/strong\u003e Part I is a revised upgrade of the first edition with additional recent results on the group of a random walk, making it relevant for readers following current developments.\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003eAdvanced mathematical tools:\u003c\/strong\u003e The authors use Riemann Surfaces and Galois Theory to present techniques that go beyond standard probabilistic methods, useful for rigorous analysis of boundary domains.\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003eApplications oriented:\u003c\/strong\u003e The monograph connects methods to applications in Stochastic Networks, Analytic Combinatorics, and Quantum Physics, helping readers see where abstract results apply.\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003eHistorical depth:\u003c\/strong\u003e The material reflects methods developed by the authors since the 1970s, providing perspective and continuity for researchers tracing the evolution of these techniques.\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003ch2\u003eWho It's For\u003c\/h2\u003e\n\u003cp\u003eThis monograph is best suited to mathematicians, theoretical probabilists, and advanced graduate students who already have a strong background in complex analysis and partial differential or functional equations and who need deep, methodical tools for two-dimensional random walks and related models.\u003c\/p\u003e\n\u003cp\u003eResearchers seeking a practical introductory text with worked exercises or readers wanting elementary introductions to probability should look elsewhere, as the book assumes mathematical maturity and focuses on algebraic and analytic methods rather than pedagogical basics.\u003c\/p\u003e\n\u003ch2\u003ePros \u0026amp; Cons\u003c\/h2\u003e\n\u003cp\u003e\u003cstrong\u003ePros\u003c\/strong\u003e\u003c\/p\u003e\n\u003cul\u003e\n\u003cli\u003eAuthoritative synthesis of decades of research that brings together complex analysis and probabilistic questions.\u003c\/li\u003e\n\u003cli\u003eClear emphasis on algebraic methods and Boundary Value Problems that are directly applicable to queueing systems and analytic combinatorics.\u003c\/li\u003e\n\u003cli\u003eRevised Part I and additional recent results make the second edition more complete for specialists following the field.\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003cp\u003e\u003cstrong\u003eCons\u003c\/strong\u003e\u003c\/p\u003e\n\u003cul\u003e\n\u003cli\u003eThe level of mathematical sophistication limits accessibility for readers without advanced training in complex function theory and related algebraic methods.\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003ch2\u003eSpecifications\u003c\/h2\u003e\n\u003ctable\u003e\n\u003ctr\u003e\n\u003ctd\u003eTitle\u003c\/td\u003e\n\u003ctd\u003eRandom Walks in the Quarter Plane: Algebraic Methods\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eEdition\u003c\/td\u003e\n\u003ctd\u003eSecond edition (revised Part I)\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eAuthors\u003c\/td\u003e\n\u003ctd\u003eGuy Fayolle, Roudolf Iasnogorodski, Vadim Malyshev\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eSubject area\u003c\/td\u003e\n\u003ctd\u003eProbability Theory and Stochastic Modelling\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eMethods used\u003c\/td\u003e\n\u003ctd\u003eComplex Function Theory, Boundary Value Problems, Riemann Surfaces, Galois Theory\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eApplications highlighted\u003c\/td\u003e\n\u003ctd\u003eStochastic Networks, Analytic Combinatorics, Quantum Physics\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003c\/table\u003e\n\u003ch2\u003eOur Verdict\u003c\/h2\u003e\n\u003cp\u003eThis is a valuable, high-level resource for specialists who need rigorous algebraic and analytic tools for two-dimensional random walks and boundary-domain problems; its revised material and long-view methodology make it good value for researchers and advanced students committed to deepening their theoretical toolkit.\u003c\/p\u003e\n\u003ch2\u003eFrequently Asked Questions\u003c\/h2\u003e\n\u003cp\u003e\u003cstrong\u003eDoes this edition add new material?\u003c\/strong\u003e\u003cbr\u003eThe second edition revises Part I and adds recent results on the group of a random walk for updated theoretical coverage.\u003c\/p\u003e\n\u003cp\u003e\u003cstrong\u003eIs the book suitable for beginners?\u003c\/strong\u003e\u003cbr\u003eNo, the book presumes advanced knowledge of complex analysis and algebraic techniques and is intended for specialists and advanced graduate students.\u003c\/p\u003e\n\u003cp\u003e\u003cstrong\u003eWhich applications does the book address?\u003c\/strong\u003e\u003cbr\u003eThe monograph connects methods to Stochastic Networks, Analytic Combinatorics, and constructions relevant to Quantum Physics.\u003c\/p\u003e","brand":"Guy Fayolle, Roudolf Iasnogorodski, Vadim Malyshev","offers":[{"title":"Default Title","offer_id":48628001210587,"sku":"331984525X","price":106.34,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0724\/1043\/1707\/files\/61YDgwUmCKL._SL1254.jpg?v=1778430112","url":"https:\/\/gearmusthave.com\/products\/331984525x","provider":"GearMustHave","version":"1.0","type":"link"}