分野別セミナー

アブストラクト：
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.