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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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The metric of the expected difference of random variables
Suppose we have a set of independent random variables $X_1,\ldots,X_n$ over $\mathbb{R}$.
It is easy to see that
$$d_{ij}=E[|X_i-X_j|]$$
satisfy the triangle inequality.
Is there any study of such me …