Diophantine approximation, fractals, and random walks on homogeneous spaces

[Math. Dept.]

February 19, 2019  16:00-17:00

W303  School of Mathematics

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SPEAKER

Barak Weiss (Tel Aviv University)

ABSTRACT

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.

SUPPORTED BY

School of Mathematics, Sichuan University