Mathematics Colloquium, CSU
Friday, April 10, 2015
3:30–4:30 pm in RT 1516
Coin Tossing and Fubini’s Nightmare
Ali Tahzibi, University of Sao Paulo at Sao Carlos, Brazil
Abstract. Flipping a coin (fair or unfair) is a very first example studied in probability
theory. If we toss a fair coin a very large number of times, with a large probability half
time we get heads. What happens, if the coin is not fair? The law of large numbers
in probability theory deals with this question. In this talk, we show the construction
(due to Katok-Milnor) of a full Lebesgue measurable subset A, of unit square and a
foliation by analytic curves in the square such that any leaf intersects A in at most
one point. The construction is related to the coin tossing of non-fair toss. Finally, we
relate the above ”pathological” example to the rigidity in dynamical systems.
* Refreshments at 3:00 PM in RT 1517