Antoine Gournay

activity

20242026

collaborators

4 papers

math.PR2026

Entropy, isoperimetry and the total variation profile of random walks

Antoine Gournay

The total variation profile $TV_{n}$ of a random walk measures how far its distribution at time $n$ is from being invariant under the generators. Three lower bounds are give…

math.GR2026

Harmonic projections, recurrent extensions and stability of the Liouville property

Antoine Gournay

The Liouville property is a strong form of amenability, but contrary to amenability, it is not well-behaved under extensions. In this paper it is shown that, for every probability…

math.GR2025

Radial isoperimetry and absence of harmonic functions with $ℓ^{p}$ -gradient

Antoine Gournay

In this paper we show that groups for which the probability of return of a random walk is bounded below by $K_{1} e x p (- K_{2} n^{c})$ have no non-constant harmonic functions with gradient…

math.GR2024

Regular maps from the lamplighter to metabelian groups

Antoine Gournay, Corentin Le Coz

We prove that the lamplighter group admits an injective Lipschitz map to any finitely generated metabelian group which is not virtually nilpotent. This implies that finitely genera…

Entropy, isoperimetry and the total variation profile of random walks

Harmonic projections, recurrent extensions and stability of the Liouville property

Radial isoperimetry and absence of harmonic functions with ℓp-gradient

Regular maps from the lamplighter to metabelian groups

Radial isoperimetry and absence of harmonic functions with $ℓ^{p}$ -gradient