Diophantine approximation, fractals, and random walks on homogeneous spaces
February 19, 2019 16:00-17:00
W303 School of Mathematics
Barak Weiss (Tel Aviv University)
A real number is normal in base D if every finite block of size k appears asymptotically in its base D expansion with the same frequency. Clearly no number in Cantor's middle thirds set is normal to base 3, but Cassels and Schmidt showed in 1950 that almost every number in the Cantor set is normal to base 2. In joint work with Simmons, Dayan and Ganguly, several easy-to-state problems of this type, which had been open for a while, have recently been solved using the analysis of random walks on homogeneous spaces. I will describe the background and explain the connection to random walks.
School of Mathematics, Sichuan University