Guillaume Aubrun

activity

20052026

most citedTensor products of convex sets and the volume of separable states on N qudits

75 citations · 508 across the 29 of their papers we have counts for

collaborators

33 papers

math.FA2026

Factorization through Lorentz cones

Guillaume Aubrun, Francesca La Piana, Alexander Müller-Hermes

A pair of proper cones $(C_{1}, C_{2})$ is said to have the Lorentz factorization property (LFP) if every $(C_{1}, C_{2})$ -positive map factors through a…

math.MG2026

Sphere Packings in Higher Dimension (after Boaz Klartag)

Guillaume Aubrun

Let $δ_{n}^{L}$ be the maximal density of a lattice sphere packing in the $n$ -dimensional Euclidean space. We explain how Boaz Klartag proved the inequality $δ_{n}^{L} \geq c n^{2} 2^{- n}$ w…

math.FA2024

Limit formulas for norms of tensor power operators

Guillaume Aubrun, Alexander Müller-Hermes

Given an operator $ϕ : X \to Y$ between Banach spaces, we consider its tensor powers $ϕ^{\otimes k}$ as operators from the $k$ -fold injective tensor product of $X$ to the $k$ -…

math.FA2024

A characterization of inner product spaces via norming vectors

Guillaume Aubrun, Mathis Cavichioli

A finite-dimensional normed space is an inner product space if and only if the set of norming vectors of any endomorphism is a linear subspace. This theorem was proved by Sain and…

math.PR2024

Optimal constants in concentration inequalities on the sphere and in the Gauss space

Guillaume Aubrun, Justin Jenkinson, Stanislaw J. Szarek

We show several variants of concentration inequalities on the sphere stated as subgaussian estimates with optimal constants. For a Lipschitz function, we give one-sided and two-sid…

math.OA2024★ 2 cited

Completely Bounded Norms of $k$ -positive Maps

Guillaume Aubrun, Kenneth R. Davidson, Alexander Müller-Hermes +2

Given an operator system $S$ , we define the parameters $r_{k} (S)$ (resp. $d_{k} (S)$ ) defined as the maximal value of the completely bounded norm of a unit…