Uniform convergence of Pfaffian point process to the Airy line ensemble
Abstract
We consider a family of Pfaffian Schur processes whose first coordinate marginal relates to the half--space geometric last passage percolation. We show that the line ensembles corresponding to the Pfaffian Schur processes with geometric weights converge uniformly over compact sets to the Airy line ensemble. By detailed asymptotic analysis of the kernels, we can verify the conditions for the finite dimensional weak convergence introduced in arXiv:2408.08445. By utilizing the tightness criteria of the line ensembles established in arXiv:2410.23899, we can further improve the finite dimensional convergence to the uniform convergence over compact sets. Moreover, using the same methodology we also show that sequences of spiked Pfaffian Schur processes converge uniformly over compact sets to the Airy wanderer line ensembles constructed in arXiv:2408.08445.
Keywords
Cite
@article{arxiv.2503.08848,
title = {Uniform convergence of Pfaffian point process to the Airy line ensemble},
author = {Zhengye Zhou},
journal= {arXiv preprint arXiv:2503.08848},
year = {2026}
}
Comments
arXiv:2503.08848 and arXiv:2510.07508 are intended to function as Part I and Part II of the same research program, and therefore share overlap in structure, notation, and introductory material