ICTP Mathematics Seminar - Wednesday, 12 October, at 14:00 (Tanja Schindler)/hybrid seminar

[ICTP/math - Di Giovannantonio Margherita]

ICTP MATHEMATICS SEMINARS 2022

Wednesday, 12 October, at 14:00

Hybrid seminar

Venue: for in-person attendees (Leonardo da Vinci, Luigi Stasi seminar 
room).

For virtual attendees:

Register in advance for this meeting:
https://zoom.us/meeting/register/tJAvf-GsqTspHdyZx3rgfg1RyiuEKtUdnq_Q
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information about joining the meeting.

Speaker: Tanja Schindler (University of Vienna, Austria)

Title: Almost sure asymptotic behaviour of Birkhoff sums for infinite 
measure-preserving dynamical systems

Abstract: We are interested in the limit behaviour of Birkhoff sums over 
an infinite sigma‐finite measure space. If the observable is integrable 
then -by a classical theorem by Aaronson‐ there exists no sequence of 
real numbers such that the Birkhoff sum normed by this sequence 
converges almost surely to l. Under strong mixing conditions on the 
underlying system we prove a generalized strong law of large numbers for 
integrable observables using a truncated sum adding a suitable number of 
terms depending on the point of evaluation. For f not integrable we give 
conditions on f such that the Birkhoff sum normed by a sequence of real 
numbers converges almost surely to l. Finally, we look at the example of 
the backwards continued fractions where we have an observab1e which is 
non-integrable wrt the measure restrictet to a finite measure set. We 
give a proper truncation also for this system. This is joint work with 
Claudio Bonanno.

https://indico.ictp.it/event/10076/