LEADER 07878nam 2201969Ia 450 001 9910781200803321 005 20200520144314.0 010 $a1-282-30380-5 010 $a9786612303807 010 $a1-4008-3106-7 024 7 $a10.1515/9781400831067 035 $a(CKB)2550000000002880 035 $a(EBL)475845 035 $a(OCoLC)507428541 035 $a(SSID)ssj0000337335 035 $a(PQKBManifestationID)11297311 035 $a(PQKBTitleCode)TC0000337335 035 $a(PQKBWorkID)10287892 035 $a(PQKB)10258020 035 $a(DE-B1597)446614 035 $a(OCoLC)979685624 035 $a(DE-B1597)9781400831067 035 $a(Au-PeEL)EBL475845 035 $a(CaPaEBR)ebr10333494 035 $a(CaONFJC)MIL230380 035 $a(MiAaPQ)EBC475845 035 $a(PPN)15099625X 035 $a(EXLCZ)992550000000002880 100 $a20090202d2009 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 14$aThe ergodic theory of lattice subgroups$b[electronic resource] /$fAlexander Gorodnik and Amos Nevo 205 $aCourse Book 210 $aPrinceton, N.J. $cPrinceton University Press$d2009 215 $a1 online resource (136 p.) 225 1 $aAnnals of mathematics studies ;$vno. 172 300 $aDescription based upon print version of record. 311 $a0-691-14184-3 311 $a0-691-14185-1 320 $aIncludes bibliographical references and index. 327 $t Frontmatter -- $tContents -- $tPreface -- $tChapter One. Main results: Semisimple Lie groups case -- $tChapter Two. Examples and applications -- $tChapter Three. Definitions, preliminaries, and basic tools -- $tChapter Four. Main results and an overview of the proofs -- $tChapter Five. Proof of ergodic theorems for S-algebraic groups -- $tChapter Six. Proof of ergodic theorems for lattice subgroups -- $tChapter Seven. Volume estimates and volume regularity -- $tChapter Eight. Comments and complements -- $tBibliography -- $tIndex 330 $aThe results established in this book constitute a new departure in ergodic theory and a significant expansion of its scope. Traditional ergodic theorems focused on amenable groups, and relied on the existence of an asymptotically invariant sequence in the group, the resulting maximal inequalities based on covering arguments, and the transference principle. Here, Alexander Gorodnik and Amos Nevo develop a systematic general approach to the proof of ergodic theorems for a large class of non-amenable locally compact groups and their lattice subgroups. Simple general conditions on the spectral theory of the group and the regularity of the averaging sets are formulated, which suffice to guarantee convergence to the ergodic mean. In particular, this approach gives a complete solution to the problem of establishing mean and pointwise ergodic theorems for the natural averages on semisimple algebraic groups and on their discrete lattice subgroups. Furthermore, an explicit quantitative rate of convergence to the ergodic mean is established in many cases. The topic of this volume lies at the intersection of several mathematical fields of fundamental importance. These include ergodic theory and dynamics of non-amenable groups, harmonic analysis on semisimple algebraic groups and their homogeneous spaces, quantitative non-Euclidean lattice point counting problems and their application to number theory, as well as equidistribution and non-commutative Diophantine approximation. Many examples and applications are provided in the text, demonstrating the usefulness of the results established. 410 0$aAnnals of mathematics studies ;$vno. 172. 606 $aErgodic theory 606 $aLie groups 606 $aLattice theory 606 $aHarmonic analysis 606 $aDynamics 610 $aAbsolute continuity. 610 $aAlgebraic group. 610 $aAmenable group. 610 $aAsymptote. 610 $aAsymptotic analysis. 610 $aAsymptotic expansion. 610 $aAutomorphism. 610 $aBorel set. 610 $aBounded function. 610 $aBounded operator. 610 $aBounded set (topological vector space). 610 $aCongruence subgroup. 610 $aContinuous function. 610 $aConvergence of random variables. 610 $aConvolution. 610 $aCoset. 610 $aCounting problem (complexity). 610 $aCounting. 610 $aDifferentiable function. 610 $aDimension (vector space). 610 $aDiophantine approximation. 610 $aDirect integral. 610 $aDirect product. 610 $aDiscrete group. 610 $aEmbedding. 610 $aEquidistribution theorem. 610 $aErgodic theory. 610 $aErgodicity. 610 $aEstimation. 610 $aExplicit formulae (L-function). 610 $aFamily of sets. 610 $aHaar measure. 610 $aHilbert space. 610 $aHyperbolic space. 610 $aInduced representation. 610 $aInfimum and supremum. 610 $aInitial condition. 610 $aInterpolation theorem. 610 $aInvariance principle (linguistics). 610 $aInvariant measure. 610 $aIrreducible representation. 610 $aIsometry group. 610 $aIwasawa group. 610 $aLattice (group). 610 $aLie algebra. 610 $aLinear algebraic group. 610 $aLinear space (geometry). 610 $aLipschitz continuity. 610 $aMass distribution. 610 $aMathematical induction. 610 $aMaximal compact subgroup. 610 $aMaximal ergodic theorem. 610 $aMeasure (mathematics). 610 $aMellin transform. 610 $aMetric space. 610 $aMonotonic function. 610 $aNeighbourhood (mathematics). 610 $aNormal subgroup. 610 $aNumber theory. 610 $aOne-parameter group. 610 $aOperator norm. 610 $aOrthogonal complement. 610 $aP-adic number. 610 $aParametrization. 610 $aParity (mathematics). 610 $aPointwise convergence. 610 $aPointwise. 610 $aPrincipal homogeneous space. 610 $aPrincipal series representation. 610 $aProbability measure. 610 $aProbability space. 610 $aProbability. 610 $aRate of convergence. 610 $aRegular representation. 610 $aRepresentation theory. 610 $aResolution of singularities. 610 $aSobolev space. 610 $aSpecial case. 610 $aSpectral gap. 610 $aSpectral method. 610 $aSpectral theory. 610 $aSquare (algebra). 610 $aSubgroup. 610 $aSubsequence. 610 $aSubset. 610 $aSymmetric space. 610 $aTensor algebra. 610 $aTensor product. 610 $aTheorem. 610 $aTransfer principle. 610 $aUnit sphere. 610 $aUnit vector. 610 $aUnitary group. 610 $aUnitary representation. 610 $aUpper and lower bounds. 610 $aVariable (mathematics). 610 $aVector group. 610 $aVector space. 610 $aVolume form. 610 $aWord metric. 615 0$aErgodic theory. 615 0$aLie groups. 615 0$aLattice theory. 615 0$aHarmonic analysis. 615 0$aDynamics. 676 $a515/.48 686 $aSI 830$2rvk 700 $aGorodnik$b Alexander$f1975-$01476747 701 $aNevo$b Amos$f1966-$01476748 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910781200803321 996 $aThe ergodic theory of lattice subgroups$93691524 997 $aUNINA LEADER 05435nam 22006374a 450 001 9910830492603321 005 20230617040512.0 010 $a1-280-28759-4 010 $a9786610287598 010 $a0-470-02531-X 010 $a0-470-02529-8 035 $a(CKB)1000000000357174 035 $a(EBL)242942 035 $a(OCoLC)607910858 035 $a(SSID)ssj0000209391 035 $a(PQKBManifestationID)11189703 035 $a(PQKBTitleCode)TC0000209391 035 $a(PQKBWorkID)10265868 035 $a(PQKB)10738734 035 $a(MiAaPQ)EBC242942 035 $a(EXLCZ)991000000000357174 100 $a20050527d2005 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aNetwork congestion control$b[electronic resource] $emanaging Internet traffic /$fMichael Welzl 210 $aChichester, West Sussex, England ;$aHoboken, NJ $cJ. Wiley$dc2005 215 $a1 online resource (283 p.) 225 1 $aWiley Series on Communications Networking & Distributed Systems 300 $aDescription based upon print version of record. 311 $a0-470-02528-X 320 $aIncludes bibliographical references (p. [243]-257) and index. 327 $aNetwork Congestion Control; Contents; Foreword; Preface; List of Tables; List of Figures; 1 Introduction; 1.1 Who should read this book?; 1.2 Contents; 1.3 Structure; 1.3.1 Reader's guide; 2 Congestion control principles; 2.1 What is congestion?; 2.1.1 Overprovisioning or control?; 2.2 Congestion collapse; 2.3 Controlling congestion: design considerations; 2.3.1 Closed-loop versus open-loop control; 2.3.2 Congestion control and flow control; 2.4 Implicit feedback; 2.5 Source behaviour with binary feedback; 2.5.1 MIMD, AIAD, AIMD and MIAD; 2.6 Stability; 2.6.1 Control theoretic modelling 327 $a2.6.2 Heterogeneous RTTs2.6.3 The conservation of packets principle; 2.7 Rate-based versus window-based control; 2.8 RTT estimation; 2.9 Traffic phase effects; 2.9.1 Phase effects in daily life; 2.10 Queue management; 2.10.1 Choosing the right queue length; 2.10.2 Active queue management; 2.11 Scalability; 2.11.1 The end-to-end argument; 2.11.2 Other scalability hazards; 2.12 Explicit feedback; 2.12.1 Explicit congestion notification; 2.12.2 Precise feedback; 2.13 Special environments; 2.14 Congestion control and OSI layers; 2.14.1 Circuits as a hindrance; 2.15 Multicast congestion control 327 $a2.15.1 Problems2.15.2 Sender- and receiver-based schemes; 2.16 Incentive issues; 2.16.1 Tragedy of the commons; 2.16.2 Game theory; 2.16.3 Congestion pricing; 2.17 Fairness; 2.17.1 Max-min fairness; 2.17.2 Utility functions; 2.17.3 Proportional fairness; 2.17.4 TCP friendliness; 2.18 Conclusion; 3 Present technology; 3.1 Introducing TCP; 3.1.1 Basic functions; 3.1.2 Connection handling; 3.1.3 Flow control: the sliding window; 3.1.4 Reliability: timeouts and retransmission; 3.2 TCP window management; 3.2.1 Silly window syndrome; 3.2.2 SWS avoidance; 3.2.3 Delayed ACKs 327 $a3.2.4 The Nagle algorithm3.3 TCP RTO calculation; 3.3.1 Ignoring ACKs from retransmissions; 3.3.2 Not ignoring ACKs from retransmissions; 3.3.3 Updating RTO calculation; 3.4 TCP congestion control and reliability; 3.4.1 Slow start and congestion avoidance; 3.4.2 Combining the algorithms; 3.4.3 Design rationales and deployment considerations; 3.4.4 Interactions with other window-management algorithms; 3.4.5 Fast retransmit and fast recovery; 3.4.6 Multiple losses from a single window; 3.4.7 NewReno; 3.4.8 Selective Acknowledgements (SACK); 3.4.9 Explicit Congestion Notification (ECN) 327 $a3.5 Concluding remarks about TCP3.6 The Stream Control Transmission Protocol (SCTP); 3.7 Random Early Detection (RED); 3.8 The ATM 'Available Bit Rate' service; 3.8.1 Explicit rate calculation; 3.8.2 TCP over ATM; 4 Experimental enhancements; 4.1 Ensuring appropriate TCP behaviour; 4.1.1 Appropriate byte counting; 4.1.2 Limited slow start; 4.1.3 Congestion window validation; 4.1.4 Robust ECN signalling; 4.1.5 Spurious timeouts; 4.1.6 Reordering; 4.1.7 Corruption; 4.2 Maintaining congestion state; 4.2.1 TCP Control Block Interdependence; 4.2.2 The Congestion Manager; 4.2.3 MulTCP 327 $a4.3 Transparent TCP improvements 330 $aAs the Internet becomes increasingly heterogeneous, the issue of congestion control becomes ever more important. In order to maintain good network performance, mechanisms must be provided to prevent the network from being congested for any significant period of time. Michael Welzl describes the background and concepts of Internet congestion control, in an accessible and easily comprehensible format. Throughout the book, not just the how, but the why of complex technologies including the Transmission Control Protocol (TCP) and Active Queue Management are explained. The text also gives 410 0$aWiley Series on Communications Networking & Distributed Systems 606 $aInternet 606 $aTelecommunication$xTraffic$xManagement 615 0$aInternet. 615 0$aTelecommunication$xTraffic$xManagement. 676 $a004.67/8 676 $a004.678 700 $aWelzl$b Michael$f1973-$01622642 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910830492603321 996 $aNetwork congestion control$93956618 997 $aUNINA