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arXiv · 2506.19454

Unimodular random graphs with Property (T) have cost one

Łukasz Grabowski·Héctor Jardón-Sánchez·Sam Mellick
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Abstract

Hutchcroft and Pete showed that countably infinite groups with Property (T) admit cost one actions, resolving a question of Gaboriau. We give a streamlined proof of their theorem, and extend it both to locally compact second countable groups and unimodular random graphs. We prove unimodular random graph analogues of the Connes--Weiss and Glasner--Weiss theorem characterising Property (T).

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BibTeXRIS

Łukasz Grabowski, Héctor Jardón-Sánchez, Sam Mellick. 2025-06-24. Unimodular random graphs with Property (T) have cost one. https://arxiv.org/abs/2506.19454

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