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Large deviations and Erdos-Renyi laws in dynamics

Hold Date 2012-03-02 16:00~2012-03-02 18:00

Place Seminar Room 7, Faculty of Mathematics building, Ito Campus

Object person  

Speaker Manfred Denker (Pennsylvania State University, USA)

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.