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Gaussian free field limit for the Airyβ line ensemble
Abstract
We prove that the centered height function of the Airyβ line ensemble converges for each β>0, under rescaling of space and time variables, towards the Gaussian free field in the half-plane. The conformal structure for GFF involves the spatial change of coordinate x↦ √(−x). The β--dependence is isolated in the field rescaling by √β. For the proofs we study the asymptotic expansions of the moments of Laplace transforms of the Airyβ line ensemble developed in our previous work with Xu.
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BibTeX
@misc{gorin2026gaussian,
title = {{Gaussian free field limit for the Airy$_β$ line ensemble}},
author = {Vadim Gorin and Lingfu Zhang},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.05852},
eprint = {2611.05852},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.05852},
}
RIS
TY - UNPB
TI - Gaussian free field limit for the Airy_β line ensemble
AU - Vadim Gorin
AU - Lingfu Zhang
PY - 2026
DA - 2026/11/04
PB - arXiv
DO - 10.48550/arxiv.2611.05852
UR - https://arxiv.org/abs/2611.05852
AB - We prove that the centered height function of the Airy_β line ensemble converges for each β>0, under rescaling of space and time variables, towards the Gaussian free field in the half-plane. The conformal structure for GFF involves the spatial change of coordinate x↦ √(−x). The β--dependence is isolated in the field rescaling by √β. For the proofs we study the asymptotic expansions of the moments of Laplace transforms of the Airy_β line ensemble developed in our previous work with Xu.
ER -