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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## 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) | |