Scientific Calendar Event

 Description Note: ICTP has suspended all educational activities for the week of 24 February as a health precaution; more details at https://www.ictp.it/about-ictp/media-centre/news/2020/2/ictp_suspend_activities.aspx Abstract: A classical problem in probability theory is to understand the behaviour of centred and scaled sums of independent identically distributed (iid) random variables. A well known result in this area is the central limit theorem which loosely states that if X_1, X_2, ... is an iid sequence of mean 0 random variables of finite variance then (1/\sqrt{n}) \sum_{j=1}^{n} X_j will converge in distribution to a Gaussian random variable. Generalisations of the central limit theorem exists for the case that the variance of the X_i is no longer finite, in this case the scaling 1/\sqrt{n} is altered and the limiting distribution may no longer be Gaussian. One may generalise even further and consider all weak limit points of the sequence (1/A_n)(\sum_{j=1}^n X_j). It turns out that under some very mild restrictions all the limit points of this sequence have distribution belonging to the same class - namely they are semi-stable. In this talk we will be interested in what happens when the iid sequence X_1, X_2, ... is replaced by a deterministic one. We will take a particular map T:[0,1] \to [0,1] (a so called wobbly intermittent map) and a function u:[0,1] \to R and replace the sequence X_1, X_2, ... with the sequence u, u \circ T, u \circ T^2, .... I will present recent work joint with M. Holland and D. Terhesiu in which we show that for all functions u belonging to wide class the sequence u, u \circ T, u \circ T^2, ... will satisfy semi-stable limit theorems.
Go to day