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Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory.
10
votes
Accepted
What time does it take for irrational rotations to hit an interval?
There is a theorem of Kesten, which roughly says, that if you take $(\theta, \theta_0)$ random, and the number of times you hit $(0, \alpha)$ in the first $N$ iterations, subtract the expected $N \tim …
4
votes
Path length of ball on tilted, perforated plane
J. Marklof and A. Strömbergsson have pretty much complete results for the distribution you're interested in - both on the plane and in higher dimensions. Check
J. Marklof and A. Strömbergsson, The d …