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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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Maximazing the joint entropy given the probability of equality

Consider 2 independent random variables $X$ and $Y$ with values in $A=\{0, 1, \ldots, q-1\}$. Suppose that $P(X=Y)$ is equal to some constant $\varepsilon$. What is the maximal entropy $H(X, Y)$? At …