Random normal matrices in the almost-circular regime

Byun, Sung‐Soo; Seo, Seong-Mi

doi:10.3150/22-bej1514

Cited by 6 publications

(2 citation statements)

References 36 publications

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“…Very recently, the scaling limits of the symplectic induced Ginibre ensemble in the almost-circular (or weakly non-unitary) regime were obtained in [18]. While the almost-Hermitian [5,39,40] and almost-circular [9,23] ensembles have the same bulk scaling limits in the complex symmetry class, those are different in the symplectic symmetry class in the vicinity of the real line due to the lack of the translation invariance; see [18] for further details.…”

Section: Introduction and Resultsmentioning

confidence: 99%

Spherical Induced Ensembles with Symplectic Symmetry

Byun¹,

Forrester²

2023

SIGMA

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We consider the complex eigenvalues of the induced spherical Ginibre ensemble with symplectic symmetry and establish the local universality of these point processes along the real axis. We derive scaling limits of all correlation functions at regular points both in the strong and weak non-unitary regimes as well as at the origin having spectral singularity. A key ingredient of our proof is a derivation of a differential equation satisfied by the correlation kernels of the associated Pfaffian point processes, thereby allowing us to perform asymptotic analysis.

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Section: Introduction and Resultsmentioning

confidence: 99%

Spherical Induced Ensembles with Symplectic Symmetry

Byun¹,

Forrester²

2023

SIGMA

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“…Coulomb gas ensembles in the presence of a hard wall have previously been considered in the literature, but so far the focus has been on large gap probabilities (or partition functions) [1, 3-5, 29, 46, 48, 50, 53] and on the local statistics [64,70,77]. We refer to [11,12,23,51,59,69] for studies of local droplets and local statistics near soft/hard edges.…”

Section: Mittag-leffler Ensembles With a Hard Wall Constraintmentioning

confidence: 99%

Exponential moments for disk counting statistics at the hard edge of random normal matrices

Ameur,

Charlier,

Cronvall

et al. 2023

J. Spectr. Theory

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We consider the multivariate moment generating function of the disk counting statistics of a model Mittag-Leffler ensemble in the presence of a hard wall. Let n be the number of points. We focus on two regimes: (a) the "hard edge regime" where all disk boundaries are at a distance of order 1 n from the hard wall, and (b) the "semi-hard edge regime" where all disk boundaries are at a distance of order 1

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Eigenvalues of truncated unitary matrices: disk counting statistics

Ameur,

Charlier,

Moreillon

2023

Monatsh Math

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Let T be an $$n\times n$$ n × n truncation of an $$(n+\alpha )\times (n+\alpha )$$ ( n + α ) × ( n + α ) Haar distributed unitary matrix. We consider the disk counting statistics of the eigenvalues of T. We prove that as $$n\rightarrow + \infty $$ n → + ∞ with $$\alpha $$ α fixed, the associated moment generating function enjoys asymptotics of the form $$\begin{aligned} \exp \big ( C_{1} n + C_{2} + o(1) \big ), \end{aligned}$$ exp ( C 1 n + C 2 + o ( 1 ) ) , where the constants $$C_{1}$$ C 1 and $$C_{2}$$ C 2 are given in terms of the incomplete Gamma function. Our proof uses the uniform asymptotics of the incomplete Beta function.

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Random normal matrices in the almost-circular regime

Cited by 6 publications

References 36 publications

Spherical Induced Ensembles with Symplectic Symmetry

Spherical Induced Ensembles with Symplectic Symmetry

Exponential moments for disk counting statistics at the hard edge of random normal matrices

Eigenvalues of truncated unitary matrices: disk counting statistics

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