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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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Lower bound for reduced variance after conditioning

Let $X$ be a random variable with variance $\tau^2$ and $Y$ be another random variable such that $Y-X$ is independent of $X$ and has mean zero and variance $\sigma^2$. (One can think of $Y$ as a noisy …