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arXiv · 2504.11115

Transient random walks on the space of lattices

Axel Péneau·Cagri Sert
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Abstract

Given $d\geq2$, we construct a Zariski-dense random walk on the space of lattices SL$_d(\mathbb{R})/$SL$_d(\mathbb{Z})$ that exhibits escape of mass. This negates the suggestion of recurrence made by Benoist [Ben14] (ICM 2014) and by B\'enard-de Saxc\'e [BS22] (also asked in [BQ12]). For any $p \in (0,1)$, we also construct such a random walk with finite $L^p$-moment which shows that the moment assumption in [BS22] is sharp.

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Axel Péneau, Cagri Sert. 2025-04-15. Transient random walks on the space of lattices. https://arxiv.org/abs/2504.11115

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