Sine beta is tail trivial

Theodoros Assiotis; Kohei Suzuki

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arXiv · 2610.10849

Sine beta is tail trivial

Theodoros Assiotis·Kohei Suzuki

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Abstract

We prove that the sine beta point process is tail trivial for every beta >0. The key ingredient in the proof is a certain uniform entropy bound, that makes use of the DLR equations of Dereudre et al. (2021) and the bounded two-point correlation density obtained by Qu and Valko (2025) and Assiotis and Najnudel (2026), that allows us to show that tail events are translation invariant. Tail triviality then follows either from the uniqueness theorem of Assiotis (2026) or from translation mixing, which we derive from the correlation estimates of Dumaz and Malvy (2026). As consequences, we obtain the following applications: (a) extremality of sine beta in the full convex class of fixed kernel Gibbs measures without stationarity and finite-energy conditions; (b) L^2-ergodicity of the associated infinite-particle reversible diffusion for every beta>0; and (c) the almost-sure collision/noncollision dichotomy with threshold beta=1 for the diffusion.

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Theodoros Assiotis, Kohei Suzuki. 2026-10-07. Sine beta is tail trivial. https://arxiv.org/abs/2610.10849

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