LEADER 04151nam 22006975 450 001 9910163995703321 005 20230810190952.0 010 $a3-319-50930-6 024 7 $a10.1007/978-3-319-50930-3 035 $a(CKB)3710000001051377 035 $a(DE-He213)978-3-319-50930-3 035 $a(MiAaPQ)EBC4800431 035 $a(PPN)198871619 035 $a(EXLCZ)993710000001051377 100 $a20170206d2017 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aRandom Walks in the Quarter Plane $eAlgebraic Methods, Boundary Value Problems, Applications to Queueing Systems and Analytic Combinatorics /$fby Guy Fayolle, Roudolf Iasnogorodski, Vadim Malyshev 205 $a2nd ed. 2017. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2017. 215 $a1 online resource (XVII, 248 p. 17 illus.) 225 1 $aProbability Theory and Stochastic Modelling,$x2199-3149 ;$v40 311 $a3-319-50928-4 320 $aIncludes bibliographical references and index. 327 $aIntroduction 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. 330 $aThis monograph aims to promote original mathematical methods to determine the invariant measure of two-dimensional random walks in domains with boundaries. Such processes arise in numerous applications and are of interest in several areas of mathematical research, such as Stochastic Networks, Analytic Combinatorics, and Quantum Physics. This second edition consists of two parts. Part I is a revised upgrade of the first edition (1999), with additional recent results on the group of a random walk. The theoretical approach given therein has been developed by the authors since the early 1970s. By using Complex Function Theory, Boundary Value Problems, Riemann Surfaces, and Galois Theory, completely new methods are proposed for solving functional equations of two complex variables, which can also be applied to characterize the Transient Behavior of the walks, as well as to find explicit solutions to the one-dimensional Quantum Three-Body Problem, or to tackle a new class of Integrable Systems. Part II borrows special case-studies from queueing theory (in particular, the famous problem of Joining the Shorter of Two Queues) and enumerative combinatorics (Counting, Asymptotics). Researchers and graduate students should find this book very useful. 410 0$aProbability Theory and Stochastic Modelling,$x2199-3149 ;$v40 606 $aProbabilities 606 $aStatistics 606 $aComputer science$xMathematics 606 $aMathematical statistics 606 $aDifference equations 606 $aFunctional equations 606 $aProbability Theory 606 $aStatistics in Engineering, Physics, Computer Science, Chemistry and Earth Sciences 606 $aProbability and Statistics in Computer Science 606 $aDifference and Functional Equations 615 0$aProbabilities. 615 0$aStatistics. 615 0$aComputer science$xMathematics. 615 0$aMathematical statistics. 615 0$aDifference equations. 615 0$aFunctional equations. 615 14$aProbability Theory. 615 24$aStatistics in Engineering, Physics, Computer Science, Chemistry and Earth Sciences. 615 24$aProbability and Statistics in Computer Science. 615 24$aDifference and Functional Equations. 676 $a519.282 700 $aFayolle$b Guy$4aut$4http://id.loc.gov/vocabulary/relators/aut$053811 702 $aIasnogorodski$b Roudolf$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aMalyshev$b Vadim$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910163995703321 996 $aRandom Walks in the Quarter Plane$92218358 997 $aUNINA