Brett Leroux

activity

20192025

collaborators

7 papers

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…

cs.CG2024

Euclidean distance compression via deep random features

Brett Leroux, Luis Rademacher

Motivated by the problem of compressing point sets into as few bits as possible while maintaining information about approximate distances between points, we construct random nonlin…

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…

math.CO2022

Expansion of random $0/1$ polytopes

Brett Leroux, Luis Rademacher

A conjecture of Mihail and Vazirani states that the edge expansion of the graph of every $0/1$ polytope is at least one. Any lower bound on the edge expansion gives an upper bound…

math.MG2021

Improved bounds for the expected number of $k$ -sets

Brett Leroux, Luis Rademacher

Given a finite set of points $S \subset R^{d}$ , a $k$ -set of $S$ is a subset $A \subset S$ of size $k$ which can be strictly separated from $S ∖ A$ by a hyperplane. S…

math.MG2019

Algebraic $k$ -sets and generally neighborly embeddings

Brett Leroux, Luis Rademacher

Given a set $S$ of $n$ points in $R^{d}$ , a $k$ -set is a subset of $k$ points of $S$ that can be strictly separated by a hyperplane from the remaining $n - k$ points. Similarl…

Expected extremal area of facets of random polytopes

Euclidean distance compression via deep random features

The minimum neighborliness of a random polytope

Estranged facets and k-facets of Gaussian random point sets

Expansion of random 0/1 polytopes

Improved bounds for the expected number of k-sets

Algebraic k-sets and generally neighborly embeddings

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

Expansion of random $0/1$ polytopes

Improved bounds for the expected number of $k$ -sets

Algebraic $k$ -sets and generally neighborly embeddings