Minas Pafis

activity

20222026

most citedThreshold for the expected measure of random polytopes

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

collaborators

9 papers

math.PR2026

Cramér transform, half-space depth and threshold phenomena for convex bodies

Minas Pafis

We study the relationship between the Cramér transform and Tukey's half-space depth for log-concave probability measures. For the uniform probability measure $μ_{K}$ on a convex body…

math.PR2026

Variance lower bounds for geometric functionals of rotationally invariant log-concave random polytopes

Minas Pafis, Christos Pandis

We establish variance lower bounds for the intrinsic volumes and the face numbers of random polytopes, generated by independent samples from rotationally invariant log-concave prob…

math.PR2026

Many Facets in Random Polytopes from Product and Log-Concave Measures

Silouanos Brazitikos, Minas Pafis

We prove bounds of order $n^{n /2} e^{O (n)}$ for the expected number of facets of high-dimensional random polytopes. First, let $μ$ be a non-degenerate compactly supported even proba…

math.MG2026

Geometry of the subgaussian body of an isotropic convex body

Apostolos Giannopoulos, Minas Pafis, Natalia Tziotziou

For a centered convex body $K \subset R^{n}$ , let $Ψ_{2} (K)$ denote the symmetric convex body whose support function is given by the $ψ_{2}$ -norms of linear functionals on $K$ . Th…

math.PR2026

Discrete log-concavity and threshold phenomena for atomic measures

Silouanos Brazitikos, Minas Pafis

We investigate threshold phenomena for random polytopes $K_N=\conv\{X_1,\dots,X_N\}$ generated by i.i.d.\ samples from an atomic law $μ$ . We identify and provide a missing justific…

math.MG2025

On the deterministic interior body of random polytopes

Minas Pafis, Natalia Tziotziou

Let ${X_{i}}_{i = 1}^{\infty}$ be a sequence of independent copies of a random vector $X$ in $R^{n}$ . We revisit the question to determine the asymptotic shape of the random p…

math.PR2023★ 3 cited

Threshold for the expected measure of the convex hull of random points with independent coordinates

Minas Pafis

Let $μ$ be an even Borel probability measure on $R$ . For every $N > n$ consider $N$ independent random vectors $X_{1}, \dots, X_{N}$ in $R^{n}$ , with indepe…

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)…