q-deformed polyanalytic Ginibre point processes:construction and central limit theorems for linear statistics
Abstract
Based on the representation theory of the q-CCR algebra, we develop a representation-theoretic construction of the q-deformed polyanalytic Fock spaces, their reproducing kernels, and the associated q-deformed polyanalytic Bargmann transforms. The associated determinantal point processes provide q-deformations of the pure and full polyanalytic Ginibre ensembles. Moreover, we determine their limiting density and establish central limit theorems for the fluctuations of their linear statistics as the number of particles tends to infinity and the deformation parameter q tends to 1 simultaneously. Remarkably, although the q-deformation changes the macroscopic density and the size of the droplet, the limiting covariance structures coincide, after spatial rescaling, with those of the classical polyanalytic Ginibre ensembles.
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BibTeX
@misc{jung2026qdeformed,
title = {{$q$-deformed polyanalytic Ginibre point processes:construction and central limit theorems for linear statistics}},
author = {Yeong-Gwang Jung and Ryosuke Sato},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.06904},
eprint = {2609.06904},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.06904},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - q-deformed polyanalytic Ginibre point processes:construction and central limit theorems for linear statistics
AU - Yeong-Gwang Jung
AU - Ryosuke Sato
PY - 2026
DA - 2026/09/07
PB - arXiv
DO - 10.48550/arxiv.2609.06904
UR - https://arxiv.org/abs/2609.06904
AB - Based on the representation theory of the q-CCR algebra, we develop a representation-theoretic construction of the q-deformed polyanalytic Fock spaces, their reproducing kernels, and the associated q-deformed polyanalytic Bargmann transforms. The associated determinantal point processes provide q-deformations of the pure and full polyanalytic Ginibre ensembles. Moreover, we determine their limiting density and establish central limit theorems for the fluctuations of their linear statistics as the number of particles tends to infinity and the deformation parameter q tends to 1 simultaneously. Remarkably, although the q-deformation changes the macroscopic density and the size of the droplet, the limiting covariance structures coincide, after spatial rescaling, with those of the classical polyanalytic Ginibre ensembles.
ER -