Brett Leroux

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20192025

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math.PR2025

Expected extremal area of facets of random polytopes

Brett Leroux, Luis Rademacher, Carsten Schütt +1

We study extremal properties of spherical random polytopes, the convex hull of random points chosen from the unit Euclidean sphere in $R^{n}$ . The extremal properties of int…

math.PR2023

The minimum neighborliness of a random polytope

Brett Leroux

Let $μ$ be a probability distribution on $R^{d}$ which assigns measure zero to every hyperplane and $S$ a set of points sampled independently from $μ$ . What can be said abou…

math.PR2023

Estranged facets and $k$ -facets of Gaussian random point sets

Brett Leroux, Luis Rademacher

Gaussian random polytopes have received a lot of attention especially in the case where the dimension is fixed and the number of points goes to infinity. Our focus is on the less s…

Expected extremal area of facets of random polytopes

The minimum neighborliness of a random polytope

Estranged facets and k-facets of Gaussian random point sets

Estranged facets and $k$ -facets of Gaussian random point sets