Several classical isoperimetric inequalities for convex sets have been extended to "empirical ones" in the last decade. In the empirical setting, a geometric quantity of a random convex set generated by samples drawn from an arbitrary distribution in the n-dimensional space is minimized (maximized) when the samples are drawn uniformly from the Euclidean ball. This talk will report some new empirical isoperimetric inequalities involving non-convex sets
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