{"product_id":"9783319509280","title":"Random Walks in the Quarter Plane : Algebraic Methods, Boundary Value Problems, Applications to Queueing Systems and Analytic Combinatorics (Probability Theory and Stochastic Modelling) (2ND)","description":"\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\u003cb\u003ePart I\u003c\/b\u003e 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 \u003ci\u003eIntegrable Systems\u003c\/i\u003e.\u003cp\u003e\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\u003cp\u003e\n\u003c\/p\u003e Introduction and History.- I The General Theory. - Probabilistic Background. - Foundations of the Analytic Approach. - The Case of a Finite Group.- II Applications to Queueing Systems and Analytic Combinatorics.- A Two-Coupled Processor Model. - References. \u003cp\u003eG. FAYOLLE: Engineer degree from École Centrale in 1967, Doctor-es-Sciences (Mathematics) from University of Paris 6, 1979. He joined INRIA in 1971. Research Director and team leader (1975-2008), now Emeritus. He has written about 100 papers in Analysis, Probability and Statistical Physics. \u003c\/p\u003e \u003cp\u003eR. IASNOGORODSKI: Doctor-es-Sciences (Mathematics) from University of Paris 6, 1979. Associate Professor in the Department of Mathematics at the University of Orléans (France), 1977-2003. He has written about 30 papers in Analysis and Probability. \u003c\/p\u003e \u003cp\u003eV.A. MALYSHEV: 1955-1961 student Moscow State University, 1967-nowadays Professor at Moscow State University, 1990-2005 Research Director at INRIA (France). He has written about 200 papers in Analysis, Probability and Mathematical Physics. \u003c\/p\u003e","brand":"Springer","offers":[{"title":"Default Title","offer_id":48803391635691,"sku":"00000_00000_00000_00000","price":201.41,"currency_code":"SGD","in_stock":true}],"url":"https:\/\/kinokuniya.com.sg\/products\/9783319509280","provider":"Books Kinokuniya Singapore","version":"1.0","type":"link"}