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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.

1 vote

An elementary probability question

YES, trivially. Even $E(\|X_0-X_1\|^2)$ is already bounded by 4x the variance. (or even 2x ?) For $n < d$, this is optimal up to a constant factor. Take the uniform distribution on the $d$ unit vecto …
Günter Rote's user avatar
  • 1,083
1 vote
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Expected minimum face angle of random convex polyhedron in $\mathbb{R}^3$

The answer is YES. (I am assuming you mean the angle between two adjacent edges on a common face. (The dihedral angles all go to $\pi$.)) The easy and brief reason is that, in a large random point set …
Günter Rote's user avatar
  • 1,083