Counterexamples to the continuous Aldous-Lyons conjecture

Tsachik Gelander

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arXiv · 2610.08581

Counterexamples to the continuous Aldous-Lyons conjecture

Tsachik Gelander

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Abstract

We construct non-co-sofic invariant random subgroups in connected simple real Lie groups of rank one with finite center, in Zariski connected simple rank-one groups over non-Archimedean local fields, and in Aut(T) for regular and bi-regular trees T. This gives a negative answer to the continuous analogue of the classical Aldous-Lyons conjecture for these groups. Our constructions build on the existence of a finitely generated non-sofic group and answer a question raised in the author's ICM paper [Gel18].

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Tsachik Gelander. 2026-10-06. Counterexamples to the continuous Aldous-Lyons conjecture. https://arxiv.org/abs/2610.08581

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