PreprintCC BY 4.0arXiv
The one percent property for free groups
Abstract
We prove that for every ε >0, there is δ>0 such that for every probability measure μ on a free group 𝔽, if the operator norm of the action of μ on L2𝔽 by convolution exceeds ε, then there is a coset of an abelian subgroup of 𝔽 with μ-mass at least δ.
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BibTeX
@misc{breuillard2026percent,
title = {{The one percent property for free groups}},
author = {Emmanuel Breuillard and Ferdinand Jacobé de Naurois},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.18106},
eprint = {2610.18106},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.18106},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The one percent property for free groups
AU - Emmanuel Breuillard
AU - Ferdinand Jacobé de Naurois
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2610.18106
UR - https://arxiv.org/abs/2610.18106
AB - We prove that for every ε >0, there is δ>0 such that for every probability measure μ on a free group 𝔽, if the operator norm of the action of μ on L^2𝔽 by convolution exceeds ε, then there is a coset of an abelian subgroup of 𝔽 with μ-mass at least δ.
ER -