Three topological phases of the elliptic Ginibre ensembles with a point charge
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913678705557504 |
|---|---|
| author | Byun, Sung-Soo Yoo, Eui |
| author_facet | Byun, Sung-Soo Yoo, Eui |
| contents | We consider the complex and symplectic elliptic Ginibre matrices of size $(c+1)N \times (c+1)N$, conditioned to have a deterministic eigenvalue at $ p \in \mathbb{R} $ with multiplicity $ c N $. We show that their limiting spectrum is either simply connected, doubly connected, or composed of two disjoint simply connected components. Moreover, denoting by $τ\in [0,1]$ the non-Hermiticity parameter, we explicitly characterise the regions in the parameter space $ (p, c, τ) $ where each topological type emerges. For cases where the droplet is either simply or doubly connected, we provide an explicit description of the limiting spectrum and the corresponding electrostatic energies. As an application, we derive the asymptotic behaviour of the moments of the characteristic polynomial for elliptic Ginibre matrices in the exponentially varying regime. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_02948 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Three topological phases of the elliptic Ginibre ensembles with a point charge Byun, Sung-Soo Yoo, Eui Mathematical Physics Complex Variables Probability We consider the complex and symplectic elliptic Ginibre matrices of size $(c+1)N \times (c+1)N$, conditioned to have a deterministic eigenvalue at $ p \in \mathbb{R} $ with multiplicity $ c N $. We show that their limiting spectrum is either simply connected, doubly connected, or composed of two disjoint simply connected components. Moreover, denoting by $τ\in [0,1]$ the non-Hermiticity parameter, we explicitly characterise the regions in the parameter space $ (p, c, τ) $ where each topological type emerges. For cases where the droplet is either simply or doubly connected, we provide an explicit description of the limiting spectrum and the corresponding electrostatic energies. As an application, we derive the asymptotic behaviour of the moments of the characteristic polynomial for elliptic Ginibre matrices in the exponentially varying regime. |
| title | Three topological phases of the elliptic Ginibre ensembles with a point charge |
| topic | Mathematical Physics Complex Variables Probability |
| url | https://arxiv.org/abs/2502.02948 |