LEADER 03586nam 2200601 450 001 9910480616203321 005 20180731044909.0 010 $a1-4704-0533-4 035 $a(CKB)3360000000465111 035 $a(EBL)3114166 035 $a(SSID)ssj0000888802 035 $a(PQKBManifestationID)11566304 035 $a(PQKBTitleCode)TC0000888802 035 $a(PQKBWorkID)10866476 035 $a(PQKB)11249441 035 $a(MiAaPQ)EBC3114166 035 $a(PPN)195418166 035 $a(EXLCZ)993360000000465111 100 $a20150416h20092009 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aBrownian Brownian motion-I /$fN. Chernov, D. Dolgopyat 210 1$aProvidence, Rhode Island :$cAmerican Mathematical Society,$d2009. 210 4$dİ2009 215 $a1 online resource (208 p.) 225 1 $aMemoirs of the American Mathematical Society,$x0065-9266 ;$vVolume 198, Number 927 300 $a"Volume 198, Number 927 (fourth of 6 numbers)." 311 $a0-8218-4282-X 320 $aIncludes bibliographical references and index. 327 $a""Contents""; ""Chapter 1. Introduction""; ""1.1. The model""; ""1.2. The container""; ""1.3. Billiard approximations""; ""Chapter 2. Statement of results""; ""2.1. Heavy disk in 'equilibrium' (linear motion)""; ""2.2. Heavy disk at rest (slow acceleration)""; ""2.3. Heavy disk of small size""; ""2.4. Comparison to previous works""; ""Chapter 3. Plan of the proofs""; ""3.1. General strategy""; ""3.2. Precise definitions""; ""3.3. Key technical results""; ""Chapter 4. Standard pairs and equidistribution""; ""4.1. Unstable vectors""; ""4.2. Unstable curves"" 327 $a""6.2. Structure of the proofs""""6.3. Short term moment estimates for V""; ""6.4. Moment estimatesa???a priori bounds""; ""6.5. Tightness""; ""6.6. Second moment""; ""6.7. Martingale property""; ""6.8. Transition to continuous time""; ""6.9. Uniqueness for stochastic differential equations""; ""Chapter 7. Fast slow particle""; ""Chapter 8. Small large particle""; ""Chapter 9. Open problems""; ""9.1. Collisions of the massive disk with the wall""; ""9.2. Longer time scales""; ""9.3. Stadia and the piston problem""; ""9.4. Finitely many particles""; ""9.5. Growing number of particles"" 327 $a""9.6. Particles of positive size""""Appendix A. Statistical properties of dispersing billiards""; ""A.1. Decay of correlations: overview""; ""A.2. Decay of correlations: extensions""; ""A.3. Large deviations""; ""A.4. Moderate deviations""; ""A.5. Nonsingularity of diffusion matrix""; ""A.6. Asymptotics of diffusion matrix""; ""Appendix B. Growth and distortion in dispersing billiards""; ""B.1. Regularity of H-curves""; ""B.2. Invariant Section Theorem""; ""B.3. The function space R""; ""Appendix C. Distortion bounds for two particle system""; ""Bibliography""; ""Index"" 410 0$aMemoirs of the American Mathematical Society ;$vVolume 198, Number 927. 606 $aDiffusion processes 606 $aBrownian movements 606 $aLimit theorems (Probability theory) 608 $aElectronic books. 615 0$aDiffusion processes. 615 0$aBrownian movements. 615 0$aLimit theorems (Probability theory) 676 $a519.2/33 700 $aChernov$b Nikolai$f1956-$0300360 702 $aDolgopyat$b Dmitry$f1972- 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910480616203321 996 $aBrownian Brownian motion-I$92262698 997 $aUNINA