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# Seminar

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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)
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.