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Peer-reviewedCC BYProbability Theory and Related Fields

Subcritical multiplicative chaos and the characteristic polynomial of the CβE

  • Gaultier Lambert1
  • Joseph Najnudel2
  1. 1KTH Royal Institute of technology, Matematik, Stockholm, Sweden
  2. 2University of Bristol, School of Mathematics, Bristol, UK
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Abstract

The goal of this article is to expand on the relationship between random matrix and multiplicative chaos theories using the integrability properties of the circular β β -ensembles. We obtain the multiplicative chaos convergence for the characteristic polynomial and eigenvalue counting function of the circular β β -ensembles throughout the subcritical phase, including negative powers. This generalizes recent results in the unitary case, [8, 40], to any β >0 β > 0 and for the eigenvalue counting field.

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Cite

BibTeXRIS
BibTeX
@article{lambert2026subcritical,
  title = {{Subcritical multiplicative chaos and the characteristic polynomial of the C$$\beta $$E}},
  author = {Gaultier Lambert and Joseph Najnudel},
  journal = {Probability Theory and Related Fields},
  year = {2026},
  month = may,
  doi = {10.1007/s00440-026-01501-0},
  url = {https://doi.org/10.1007/s00440-026-01501-0},
  note = {CC BY},
}
RIS
TY  - JOUR
TI  - Subcritical multiplicative chaos and the characteristic polynomial of the CβE
AU  - Gaultier Lambert
AU  - Joseph Najnudel
PY  - 2026
DA  - 2026/05/28
JO  - Probability Theory and Related Fields
DO  - 10.1007/s00440-026-01501-0
UR  - https://doi.org/10.1007/s00440-026-01501-0
AB  - The goal of this article is to expand on the relationship between random matrix and multiplicative chaos theories using the integrability properties of the circular β β -ensembles. We obtain the multiplicative chaos convergence for the characteristic polynomial and eigenvalue counting function of the circular β β -ensembles throughout the subcritical phase, including negative powers. This generalizes recent results in the unitary case, [8, 40], to any β >0 β > 0 and for the eigenvalue counting field.
SN  - 0178-8051
SN  - 1432-2064
ER  -