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<p>We construct a one-parameter family of infinite line ensembles on <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\([0, \infty )\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">[</mo> <mn>0</mn> <mo>,</mo> <mi>∞</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> 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).</p>

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Half-space Airy line ensembles

  • 期刊论文

  • 发表日期：

    2026年2月24日

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  • Evgeni Dimitrov,
  • Zongrui Yang

摘要

We construct a one-parameter family of infinite line ensembles on \([0, \infty )\) [ 0 , ∞ ) 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).