Guillaume Aubrun

activity

20242026

collaborators

6 papers

math.FA2026

Factorization through Lorentz cones

Guillaume Aubrun, Francesca La Piana, Alexander MÃ¼ller-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 $I^´_{n}^{L}$ be the maximal density of a lattice sphere packing in the $n$ -dimensional Euclidean space. We explain how Boaz Klartag proved the inequality $I^´_{n}^{L} \geq c n^{2} 2^{- n}$ …

quant-ph2025

Monogamy of entanglement between cones

Guillaume Aubrun, Alexander MÃ¼ller-Hermes, Martin PlÃ¡vala

A separable quantum state shared between parties $A$ and $B$ can be symmetrically extended to a quantum state shared between party $A$ and parties $B_{1}, \dots, B_{k}$ for every $k\in…

math.FA2025

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.FA2024

Limit formulas for norms of tensor power operators

Guillaume Aubrun, Alexander MÃ¼ller-Hermes

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

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…