summary:
Large deviation theory aims to find the exact power of decay of small random events.
Such results are well known in probability for a long time but became of interest in
ergodic theory only twenty years ago. Such results enable to derive an ergodic theorem
type result by taking maximal averages of length $O(\log n)$ starting at any time in the
orbit of a point up to time $n$:
$$ \lim_{n\to\infty} \max_{1\le k\le n-[c\log n]} \frac 1{[c\log n]} (f(T^k(x))+...+f(T^{k+[c\log n]-1)(x)$$
where $[z]$ denotes the Gauss bracket.
In this talk I will discuss some older known results and will present new results obtained with M. Nicol.
744 Motooka, Nishi-ku
Fukuoka 819-0395, Japan
TEL (Office): +81-92-802-4402
FAX (Office): +81-92-802-4405
IMI(Institute of Mathematics for Industry)
Seminar
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Today and tomorrow's seminars(0) |
Large deviations and Erdos-Renyi laws in dynamics
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Hold Date | 2012-03-02 16:00~2012-03-02 18:00 |
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Place | Seminar Room 7, Faculty of Mathematics building, Ito Campus |
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Speaker | Manfred Denker (Pennsylvania State University, USA) |