PreprintCC BY 4.0arXiv
Almost-optimal bulk regularity conditions in the CLT for GβE
Abstract
We consider linear statistics ∑k=1N f(xk) of a Gaussian b-ensemble. Following the work of \cite{LaSo22}, which was concerned only with Wigner matrices, we extend their results for general b. In particular, we show that the CLT holds for any f ∈ H1/2 + e. The novel input which was not used in \cite{LaSo22} is the Helffer-Sjöstrand representation for the covariance, first appearing the random matrix context in \cite{ErYa15}, coupled with characteristic flow estimates for DBM, first appearing in \cite{Bo22}.
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BibTeX
@misc{zhang2026almostoptimal,
title = {{Almost-optimal bulk regularity conditions in the CLT for G$β$E}},
author = {Albert Zhang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.24211},
eprint = {2610.24211},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.24211},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Almost-optimal bulk regularity conditions in the CLT for GβE
AU - Albert Zhang
PY - 2026
DA - 2026/10/16
PB - arXiv
DO - 10.48550/arxiv.2610.24211
UR - https://arxiv.org/abs/2610.24211
AB - We consider linear statistics ∑_k=1^N f(x_k) of a Gaussian b-ensemble. Following the work of \cite{LaSo22}, which was concerned only with Wigner matrices, we extend their results for general b. In particular, we show that the CLT holds for any f ∈ H^1/2 + e. The novel input which was not used in \cite{LaSo22} is the Helffer-Sjöstrand representation for the covariance, first appearing the random matrix context in \cite{ErYa15}, coupled with characteristic flow estimates for DBM, first appearing in \cite{Bo22}.
ER -