Skip to content
DraconiticResearch
Search Sources API
203,203 studies31 sourcesUpdated 50 min ago
PreprintCC BY 4.0arXiv

Asymptotics for partition functions of random normal matrix models with singularities

  • Kohei Noda
Open at sourcePDFDOICite

Abstract

We study determinantal planar Coulomb gases with a smooth radial potential, a smooth radial perturbation, jump-type singularities (including the bulk, semi-hard, hard, and soft-edge regimes), and a hard wall region given by a centered disk, a disk complement, or an annulus. We obtain explicit asymptotic expansions of the partition functions up to and including the term of order $1$. Our results unify and generalize many of the earlier works.

Related

  1. Partition Functions of Two-Dimensional Coulomb Gases with Circular Root- and Jump-Type Singularities
    Kohei Noda
    Symmetry, Integrability and Geometry: Methods and ApplicationsPeer-reviewedCC BY-SA 4.0Mathematical physicsCrossref
  2. Normal and Lognormal Asymptotics for Lattice-Point Counts in Random Translates of High-Dimensional Balls
    Xin Hang Ji
    arXivPreprintarXiv licenceFull textAlgebra & number theoryProbabilityarXiv
  3. Inequalities and asymptotics for hook numbers in two partition functions of MacMahon and Andrews
    Rupam Barman, Archit Deb, Sayantan Ghorai
    arXivPreprintarXiv licenceFull textAlgebra & number theoryCombinatorics & discrete mathematicsarXiv
  4. On partition functions of Gaussian random variables
    Omer Friedland, Olivier Guédon, Fabien Souli
    HALPreprintCC BY-NC-ND 4.0Full textAnalysis & PDEsProbabilityHALarXiv
  5. Uniform Asymptotics for Andrews-Beck Partition Statistics
    Renrong Mao
    arXivPreprintarXiv licenceFull textCombinatorics & discrete mathematicsarXiv

Cite

BibTeXRIS
BibTeX
@misc{noda2026asymptotics,
  title = {{Asymptotics for partition functions of random normal matrix models with singularities}},
  author = {Kohei Noda},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.25307},
  eprint = {2609.25307},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.25307},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Asymptotics for partition functions of random normal matrix models with singularities
AU  - Kohei Noda
PY  - 2026
DA  - 2026/09/21
PB  - arXiv
DO  - 10.48550/arxiv.2609.25307
UR  - https://arxiv.org/abs/2609.25307
AB  - We study determinantal planar Coulomb gases with a smooth radial potential, a smooth radial perturbation, jump-type singularities (including the bulk, semi-hard, hard, and soft-edge regimes), and a hard wall region given by a centered disk, a disk complement, or an annulus. We obtain explicit asymptotic expansions of the partition functions up to and including the term of order $1$. Our results unify and generalize many of the earlier works.
ER  -