4 papers
Entropy, isoperimetry and the total variation profile of random walks
Antoine Gournay
The total variation profile of a random walk measures how far its distribution at time is from being invariant under the generators. Three lower bounds are give…
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…
Radial isoperimetry and absence of harmonic functions with -gradient
Antoine Gournay
In this paper we show that groups for which the probability of return of a random walk is bounded below by have no non-constant harmonic functions with gradient…
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…