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001 978-3-319-50930-3
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020 _a9783319509303
_9978-3-319-50930-3
024 7 _a10.1007/978-3-319-50930-3
_2doi
040 _aISI Library, Kolkata
050 4 _aQA273.A1-274.9
050 4 _aQA274-274.9
072 7 _aPBT
_2bicssc
072 7 _aMAT029000
_2bisacsh
072 7 _aPBT
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072 7 _aPBWL
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082 0 4 _a519.2
_223
100 1 _aFayolle, Guy.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aRandom Walks in the Quarter Plane
_h[electronic resource] :
_bAlgebraic Methods, Boundary Value Problems, Applications to Queueing Systems and Analytic Combinatorics /
_cby Guy Fayolle, Roudolf Iasnogorodski, Vadim Malyshev.
250 _a2nd ed. 2017.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Springer,
_c2017.
300 _aXVII, 248 p. 17 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aProbability Theory and Stochastic Modelling,
_x2199-3130 ;
_v40
505 0 _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.
520 _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.
650 0 _aDistribution (Probability theory.
650 0 _aStatistics.
650 0 _aComputer science.
650 0 _aFunctional equations.
650 1 4 _aProbability Theory and Stochastic Processes.
_0http://scigraph.springernature.com/things/product-market-codes/M27004
650 2 4 _aStatistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences.
_0http://scigraph.springernature.com/things/product-market-codes/S17020
650 2 4 _aProbability and Statistics in Computer Science.
_0http://scigraph.springernature.com/things/product-market-codes/I17036
650 2 4 _aDifference and Functional Equations.
_0http://scigraph.springernature.com/things/product-market-codes/M12031
700 1 _aIasnogorodski, Roudolf.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
700 1 _aMalyshev, Vadim.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783319509280
776 0 8 _iPrinted edition:
_z9783319509297
776 0 8 _iPrinted edition:
_z9783319845258
830 0 _aProbability Theory and Stochastic Modelling,
_x2199-3130 ;
_v40
856 4 0 _uhttps://doi.org/10.1007/978-3-319-50930-3
912 _aZDB-2-SMA
942 _cEB
950 _aMathematics and Statistics (Springer-11649)
999 _c427039
_d427039