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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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Concentration for sum of order statistics
Assume we draw $n$ numbers uniform i.i.d. from $[0,1]$, and let the least $k$ of them be $x_1,\dots,x_k$. It is well-known that their expectations are $\frac{1}{n+1},\dots,\frac{k}{n+1}$, so the expec …