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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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Integrability of Gaussian sums
It is a standard fact from the theory of Gaussian processes (see e.g. the Ledoux-Talagrand book)
that if $X_s$, $s \in S$, is a (centered) Gaussian process such that
$Z = \sup_s X_s$ is finite almost …