- Microscopic chaos from Brownian motion? C. P. Dettmann, E. G. D. Cohen and H. van Beijeren, Nature
**401,**875-875 (1999) ps.gz (1.0M when uncompressed) arxiv - The existence of Burnett coefficients in the periodic Lorentz gas, N. I. Chernov and C. P. Dettmann, Physica A
**279,**37-44 (2000) ps arxiv - Microscopic chaos and diffusion C. P. Dettmann and E. G. D. Cohen, J. Stat. Phys.
**101,**775-817 (2000) ps.gz (28 pages; 2.1M when uncompressed) arxiv - Note on chaos and diffusion C. P. Dettmann and E. G. D. Cohen, J. Stat. Phys.
**103,**589-599 (2001) ps arxiv - The Burnett expansion of the periodic Lorentz gas, C. P. Dettmann, Ergod. Th. Dyn. Sys.
**23,**481-491 (2003) ps arxiv - Peeping at chaos: Nondestructive monitoring of chaotic systems by measuring long-time escape rates L. A. Bunimovich and C. P. Dettmann, EPL,
**80**40001 (2007). pdf arxivanimation (6.1M) - Product of
*n*independent uniform random variables, C. P. Dettmann and O. Georgiou, Stat. Prob. Lett.,**79**, 2501-2503 (2009). pdf - New horizons in multidimensional diffusion: The Lorentz gas and the Riemann Hypothesis, C. P. Dettmann, J. Stat. Phys.
**146**181-204 (2012). pdf arxiv animation (4.8M) - Escape through a time-dependent hole in the doubling map, A. L. P. Livorati, O. Georgiou, C. P. Dettmann and E. D. Leonel, Phys. Rev. E,
**89**052913 (2014). arxiv pdf - Book chapter: The Lorentz gas as a paradigm for nonequilibrium stationary states, C. P. Dettmann, pp 315-365 in Hard ball systems and the Lorentz gas (edited by D. Szasz), Encyclopaedia of Mathematical Sciences Vol 101 (Springer, 2000). Full size version, 50 pages pdf. Environmental microscopic version, 25 pages pdf.

Correlation functions as used in dynamical systems give the average of products of observables at different times. For (multiple) mixing systems the correlation functions approach in the long time limit the products of the averages of (more than) two observables, and for observables defined by relatively smooth functions this can be characterised by the rate of decay of (multiple) correlations. The papers below express properties such as diffusion and escape rates of the Lorentz gas and open systems in terms of correlations, and in some cases use correlation decay results to show that these properties are well defined. See the animation below.

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