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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.

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Random versions of deterministic problems

Lets say you want to know if $\sum_n^\infty sin(a_n)$ converges for some set of values $a_n$. In many cases it might be really hard to prove (if not impossible) that $a_n\mod \pi$ eventually is not re …