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Globus Seminar
September 20, 2012 15:40, Moscow, IUM (Bolshoi Vlas'evskii per., 11)

A random walk driven by irrational rotation

Omri Sarig

Weizmann Institute of Science, Rehovot
 Video records: Flash Video 399.2 Mb Flash Video 334.8 Mb MP4 334.8 Mb MP4 399.2 Mb

Abstract: Let $\alpha$ be an irrational multiple of $\pi$, and place a “walker” at the origin of $Z$. Pick a point $x$ randomly uniformly on the unit circle, and start rotating it by the angle alpha. Every time the point falls in the top half of the circle, move the walker one step to the right, and every time the point falls in the bottom half of the circle, move the walker one step to the left. For special values of $\alpha$, we give detailed analysis of the number of time the walker returns to 0 up to time $n$.