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PreprintCC BY 4.0arXiv

Airy limit for the Jack process and topological expansion

  • Jiaming Xu
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Abstract

For every β>0, we establish multi-time soft-edge moment convergence for a class of Jack processes, including the Jack--Plancherel process, a discrete β-analogue of Dyson Brownian motion. The limiting moments admit an absolutely convergent expansion in terms of nonnegative Brownian bridges decorated by pairs of equal and opposite jumps. At equal times, we identify this limit with the joint Laplace statistics of the Airyβ process for β≥1. The same Brownian expansion yields an asymptotic β-topological expansion of the marginal b-conjecture and, at β=2, an explicit nonnegative formula for the Witten--Kontsevich intersection numbers.

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Cite

BibTeXRIS
BibTeX
@misc{xu2026airy,
  title = {{Airy limit for the Jack process and topological expansion}},
  author = {Jiaming Xu},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2609.03532},
  eprint = {2609.03532},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.03532},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Airy limit for the Jack process and topological expansion
AU  - Jiaming Xu
PY  - 2026
DA  - 2026/10/25
PB  - arXiv
DO  - 10.48550/arxiv.2609.03532
UR  - https://arxiv.org/abs/2609.03532
AB  - For every β>0, we establish multi-time soft-edge moment convergence for a class of Jack processes, including the Jack--Plancherel process, a discrete β-analogue of Dyson Brownian motion. The limiting moments admit an absolutely convergent expansion in terms of nonnegative Brownian bridges decorated by pairs of equal and opposite jumps. At equal times, we identify this limit with the joint Laplace statistics of the Airy_β process for β≥1. The same Brownian expansion yields an asymptotic β-topological expansion of the marginal b-conjecture and, at β=2, an explicit nonnegative formula for the Witten--Kontsevich intersection numbers.
ER  -