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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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Anti-concentration for sums of geometric random variables
Consider the random variable $Y = Y_1 + \dots + Y_k$, where each $Y_i$ is iid distributed as a geometric random variable with sucess probability $p$; here we should think of $p$ as being close to zero …