Asymptotics of Jack measures with homogeneous specializations

Fuente: arXiv
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Hauptverfasser: Dimitrov, Evgeni, Gao, Xiaohan, Gu, Andy, Niedernhofer, Ryan
Format: Preprint
Veröffentlicht: 2025
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author Dimitrov, Evgeni
Gao, Xiaohan
Gu, Andy
Niedernhofer, Ryan
author_facet Dimitrov, Evgeni
Gao, Xiaohan
Gu, Andy
Niedernhofer, Ryan
contents We consider Jack measures on partitions with homogeneous defining specializations. For each of the six distinct classes of measures obtained this way we prove a global law of large numbers with an explicit limiting particle density. We also demonstrate for one of these classes how to obtain a global central limit theorem, global and edge large deviation principles, and edge universality using the results of the paper. Our argument is based on explicitly evaluating Jack symmetric functions at homogeneous specializations, relating the Jack measures to the discrete $β$-ensembles from (Publications math{\' e}matiques de l'IH{\' E}S 125, 1-78, 2017) and using the discrete loop equations to substantially reduce computations.
format Preprint
id arxiv_https___arxiv_org_abs_2509_09814
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Asymptotics of Jack measures with homogeneous specializations
Dimitrov, Evgeni
Gao, Xiaohan
Gu, Andy
Niedernhofer, Ryan
Probability
Mathematical Physics
82B05, 60F10
We consider Jack measures on partitions with homogeneous defining specializations. For each of the six distinct classes of measures obtained this way we prove a global law of large numbers with an explicit limiting particle density. We also demonstrate for one of these classes how to obtain a global central limit theorem, global and edge large deviation principles, and edge universality using the results of the paper. Our argument is based on explicitly evaluating Jack symmetric functions at homogeneous specializations, relating the Jack measures to the discrete $β$-ensembles from (Publications math{\' e}matiques de l'IH{\' E}S 125, 1-78, 2017) and using the discrete loop equations to substantially reduce computations.
title Asymptotics of Jack measures with homogeneous specializations
topic Probability
Mathematical Physics
82B05, 60F10
url https://arxiv.org/abs/2509.09814