Antoine Song

collaborators

3 papers

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.DG2025

Random harmonic maps into spheres

Antoine Song

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

math.DG2025

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…