Limit theorems in dynamical systems using the spectral method. (English) Zbl 1376.37016
Dolgopyat, Dmitry (ed.) et al., Hyperbolic dynamics, fluctuations and large deviations. Special semester on hyperbolic dynamics, large deviations and fluctuations, January – June 2013, Centre Interfacultaire Bernoulli, École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland. Proceedings. Providence, RI: American Mathematical Society (AMS) (ISBN 978-1-4704-1112-1/hbk; 978-1-4704-2266-0/ebook). Proceedings of Symposia in Pure Mathematics 89, 161-193 (2015).
While the most versatile approaches to prove the central limit theorem for square-integrable independent random variables are probably those relying on martingale arguments, the present text is devoted to the approach that is generally used in first-year probability courses, relying on characteristic functions. This powerful spectral method was devised to study Markov chains and adapted to the context of deterministic dynamical systems.
For the entire collection see [Zbl 1314.37007].
For the entire collection see [Zbl 1314.37007].
Reviewer: George Stoica (Saint John)
MSC:
| 37A50 | Dynamical systems and their relations with probability theory and stochastic processes |
| 37A30 | Ergodic theorems, spectral theory, Markov operators |
| 37D25 | Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.) |
| 37C30 | Functional analytic techniques in dynamical systems; zeta functions, (Ruelle-Frobenius) transfer operators, etc. |
| 60F05 | Central limit and other weak theorems |
