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Half-space Airy line ensembles
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DOI：10.1007/s00440-026-01469-x.png)
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Abstract
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We construct a one-parameter family of infinite line ensembles on [0,infinity)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$[0, \infty )$$\end{document} that are natural half-space analogues of the Airy line ensemble. Away from the origin these ensembles are locally described by avoiding Brownian bridges, and near the origin they are described by a sequence of avoiding reverse Brownian motions with alternating drifts, that depend on the parameter of the model. In addition, the restrictions of our ensembles to finitely many vertical lines form Pfaffian point processes with the crossover kernels obtained by Baik-Barraquand-Corwin-Suidan (Baik et al., Ann. Probab. 46(6):3015-3089, 2018).
Keywords:
SCHUR PROCESS
PARTIAL SUMS
APPROXIMATION
ASYMPTOTICS
UNITARY
THEOREM
LIMIT
MODEL
EDGE
ASEP
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1.6
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