Minas Pafis

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20222026

most citedThreshold for the expected measure of random polytopes

6 citations · 9 across the 8 of their papers we have counts for

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Showing 2022 · math.PRShow all

2 papers · 2 filters

math.PR2022★ 6 cited

Threshold for the expected measure of random polytopes

Silouanos Brazitikos, Apostolos Giannopoulos, Minas Pafis

Let $μ$ be a log-concave probability measure on $R^{n}$ and for any $N > n$ consider the random polytope $K_{N} = conv {X_{1}, \dots, X_{N}}$ , where $X_{1}, X_{2}, \dots$ are inde…

math.PR2022

Half-space depth of log-concave probability measures

Silouanos Brazitikos, Apostolos Giannopoulos, Minas Pafis

Given a probability measure $μ$ on $R^{n}$ , Tukey's half-space depth is defined for any $x \in R^{n}$ by $φ_{μ} (x) = in f {μ (H) : H \in H (x)}$ , where ${\cal H}(x)…