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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 walks and Lyapunov exponents
Given a sequence $Y_1, Y_2, \dots$ of i.i.d. matrices in $\mathrm{GL}_n(\mathbb R)$, there is a theorem of Furstenberg and Kesten which says that if $\mathbb E(\log\|Y_1\|)$ is finite, there exists a …