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arXiv · 2610.18106

The one percent property for free groups

Emmanuel Breuillard·Ferdinand Jacobé de Naurois
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Abstract

We prove that for every $\varepsilon >0$, there is $δ>0$ such that for every probability measure $μ$ on a free group $\mathbb{F}$, if the operator norm of the action of $μ$ on $L^2\mathbb{F}$ by convolution exceeds $\varepsilon$, then there is a coset of an abelian subgroup of $\mathbb{F}$ with $μ$-mass at least $δ$.

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Emmanuel Breuillard, Ferdinand Jacobé de Naurois. 2026-10-13. The one percent property for free groups. https://arxiv.org/abs/2610.18106

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