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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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Covariance inequality with Lipschitz functions

Suppose that $X$ and $Y$ are random variables and suppose that for all Lipschitz functions $f$ and $g$ s.t. $f(X),g(Y)\in L^p$, $p>2$, $$ |\operatorname{Cov}(f(X),g(Y))|\le \big(\operatorname{Lip}(f)\ …