Sine beta is tail trivial
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.
Related
BibTeX
@misc{assiotis2026sine,
title = {{Sine beta is tail trivial}},
author = {Theodoros Assiotis and Kohei Suzuki},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.10849},
eprint = {2610.10849},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.10849},
}
RIS
TY - UNPB
TI - Sine beta is tail trivial
AU - Theodoros Assiotis
AU - Kohei Suzuki
PY - 2026
DA - 2026/10/07
PB - arXiv
DO - 10.48550/arxiv.2610.10849
UR - https://arxiv.org/abs/2610.10849
AB - 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.
ER -