Antoine Song

activity

20232026

collaborators

5 papers

math.PR2026

A very short proof of the subgaussian convex-order comparison theorem

Antoine Song, Michel Talagrand

We provide a very short proof of the following comparison theorem, which has recently played an important role: every centered subgaussian random vector is dominated in convex orde…

math.PR2026

On Talagrand's Convexity Conjecture

Dongming Merrick Hua, Antoine Song, Stefan Tudose

We prove that any random vector in $R^{n}$ which is dominated in convex order by a standard Gaussian vector can be written as the sum of three standard Gaussian vectors. Thi…

math.DG2024

Hyperbolic groups and spherical minimal surfaces

Antoine Song

Let $M$ be a closed, oriented, negatively curved, $n$ -dimensional manifold with fundamental group $Γ$ . Let $S^{\infty}$ be the unit sphere in $ℓ^{2} (Γ)$ , on which $Γ$ acts by the re…

math.DG2024

Random harmonic maps into spheres

Antoine Song

Let $S$ be a punctured Riemann surface with Euler characteristic $χ (S) < 0$ . For any unitary representation $ρ : π_{1} (S) \to U (N)$ , we introduce its renormalized energy and its harmoni…

math.DG2023

Scalar curvature and volume entropy of hyperbolic 3-manifolds

Demetre Kazaras, Antoine Song, Kai Xu

We show that any closed hyperbolic 3-manifold M admits a Riemannian metric with scalar curvature at least -6, but with volume entropy strictly larger than 2. In particular, this co…