PreprintarXiv licencearXiv
A large deviation principle for the Gaussian beta ensemble in the high temperature regime
Abstract
We show a large deviation principle for the weighted spectral measure of the Gaussian beta ensemble in the high temperature regime, when nβn→ 2c ∈ [0,∞). The resulting rate function has a novel and interesting structure: it is finite only for discrete measures and moreover, in the very high-temperature regime (when c=0), additional terms may arise that penalize each support point beyond the first.
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BibTeX
@misc{gotz2026large,
title = {{A large deviation principle for the Gaussian beta ensemble in the high temperature regime}},
author = {Helene Götz and Jan Nagel},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.24731},
eprint = {2609.24731},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.24731},
}
RIS
TY - UNPB
TI - A large deviation principle for the Gaussian beta ensemble in the high temperature regime
AU - Helene Götz
AU - Jan Nagel
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2609.24731
UR - https://arxiv.org/abs/2609.24731
AB - We show a large deviation principle for the weighted spectral measure of the Gaussian beta ensemble in the high temperature regime, when nβ_n→ 2c ∈ [0,∞). The resulting rate function has a novel and interesting structure: it is finite only for discrete measures and moreover, in the very high-temperature regime (when c=0), additional terms may arise that penalize each support point beyond the first.
ER -