Brownian Brownian motion-I / / N. Chernov, D. Dolgopyat

• Record Nr.: UNINA9910829176503321
• Autore: Chernov Nikolai <1956->
• Pubbl/distr/stampa: Providence, Rhode Island : , : American Mathematical Society, , 2009; ©2009
• ISBN: 1-4704-0533-4
• Descrizione fisica: 1 online resource (208 p.)
• Collana: Memoirs of the American Mathematical Society, , 0065-9266 ; ; Volume 198, Number 927
• Disciplina: 519.2/33
• Soggetti: Diffusion processes; Brownian movements; Limit theorems (Probability theory)
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: "Volume 198, Number 927 (fourth of 6 numbers)."
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: ""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""; ""6.2. Structure of the proofs""""6.3. Short term moment estimates for V""; ""6.4. Moment estimatesâ€?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""; ""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""