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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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An inequality based on expectation of continuous random variables

You can prove this working backwards from your last expression: $(y - x)^2 g(x) g(y) f(x) f(y) > 0$, now if you expand this term you obtain $g(x) f(x) y^2 g(y) f(y) + x^2 g(x) f(x) g(y) f(y) \geq …
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5 votes
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assumptions on local rademacher complexities

A lot of the work on Local Rademacher complexities of Koltchinskii, and Bartlett for fast rates of convergence is based on Bousquet's version of Talagrand's inequality [1] (Theorem 2.11). However the …
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3 votes

What is the distribution of the maximum nearest-neighbor distance of a point cloud sampled f...

You can make the calculations for a cube with the $L_\infty$ distance and the uniform distribution and you simplify the problem a little bit by letting $X_i$ be independent of $Y_i$ you can say the f …
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