References
Introduction to metric entropy.
Introduction to metric entropy.
Entropy theory for endomorphisms of probability spaces goes back to Kolmogorov on one hand and to Shannon on the other. A pleasant introduction that resists the injuries of time is the monograph
- Patrick Billingsley: Ergodic theory and information.
Most modern monographs in ergodic theory include a section on entropy. A point which we did not touch is the Shannon-Breiman-McMillan Theorem. For a short account that includes the a proof of Doob's martingale theorem see
- Meir Smorodinsky: Ergodic Theory and Entropy, Springer LNM 214.
For an historical survey filled with personal recollections:
- Anatole Katok : Fifty Years of Entropy in Dynamics: 1958–2007
Furstenberg on noncommuting random products.
Furstenberg on noncommuting random products.
- Furstenberg et Kesten: Products of Random Matrices, Ann. Math. Statist. Volume 31, Number 2 (1960), 457-469.
- Furstenberg: Noncommuting random products, Trans. Amer. Math. Soc. 108 (1963), 377-428
- Bougerol and Lacroix: Products of random matrices with applications to Schrodinger operators, Birkhäuser, 1985
Non commutative ergodic theorems
Non commutative ergodic theorems
- M. Viana: Lectures on Lyapunov exponents, Cambridge University Press, cop. 2014
- A. Karlsson, F. Ledrappier: On laws of large numbers for random walks
- A. Karlsson, F. Ledrappier: Noncommutative Ergodic Theorems