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PreprintarXiv licencearXiv

The periodic Airy line ensembles

  • Evgeni Dimitrov
  • Samir Sarieddine
  • Zongrui Yang
  • Zhengye Zhou
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Abstract

In this paper we construct a one-parameter family of periodic Airy line ensembles π’œper,R for R>0 as weak scaling limits of Borodin's periodic Schur processes. We establish several properties of π’œper,R, including a determinantal point process structure with an explicit correlation kernel. We also show that, after a parabolic shift and normalization, π’œper,R satisfies, on its domain $[-R/2,R/2]$, the same Brownian Gibbs property enjoyed by the usual Airy line ensemble. A main technical contribution of the paper is a general tightness criterion for determinantal line ensembles, which extends the argument used by Johansson in [Comm. Math. Phys. 242 (2003), 277-329] to prove a functional limit theorem for the discrete polynuclear growth model.

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Cite

BibTeXRIS
BibTeX
@misc{dimitrov2026periodic,
  title = {{The periodic Airy line ensembles}},
  author = {Evgeni Dimitrov and Samir Sarieddine and Zongrui Yang and Zhengye Zhou},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.16611},
  eprint = {2610.16611},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.16611},
}
RIS
TY  - UNPB
TI  - The periodic Airy line ensembles
AU  - Evgeni Dimitrov
AU  - Samir Sarieddine
AU  - Zongrui Yang
AU  - Zhengye Zhou
PY  - 2026
DA  - 2026/10/12
PB  - arXiv
DO  - 10.48550/arxiv.2610.16611
UR  - https://arxiv.org/abs/2610.16611
AB  - In this paper we construct a one-parameter family of periodic Airy line ensembles π’œ^per,R for R>0 as weak scaling limits of Borodin's periodic Schur processes. We establish several properties of π’œ^per,R, including a determinantal point process structure with an explicit correlation kernel. We also show that, after a parabolic shift and normalization, π’œ^per,R satisfies, on its domain $[-R/2,R/2]$, the same Brownian Gibbs property enjoyed by the usual Airy line ensemble. A main technical contribution of the paper is a general tightness criterion for determinantal line ensembles, which extends the argument used by Johansson in [Comm. Math. Phys. 242 (2003), 277-329] to prove a functional limit theorem for the discrete polynuclear growth model.
ER  -