Hole probabilities and overcrowding estimates for products of complex Gaussian matrices

DOI10.1007/s10955-013-0750-8zbMath1314.15026arXiv1211.1576OpenAlexW3104337300MaRDI QIDQ359579

Eugene Strahov, Gernot Akemann

Publication date: 12 August 2013

Published in: Journal of Statistical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1211.1576

zbMATH Keywords

determinantal processesgeneralized Ginibre ensembleshole probabilitiesnon-Hermitian random matrix theoryovercrowdingproducts of random matrices

Mathematics Subject Classification ID

Random matrices (probabilistic aspects) (60B20) Eigenvalues, singular values, and eigenvectors (15A18) Random matrices (algebraic aspects) (15B52) Hypergeometric integrals and functions defined by them ((E), (G), (H) and (I) functions) (33C60)

Related Items (17)

Dropping the independence: singular values for products of two coupled random matrices ⋮ Hole probabilities for \(\beta\)-ensembles and determinantal point processes in the complex plane ⋮ Permanental processes from products of complex and quaternionic induced Ginibre ensembles ⋮ Polynomial ensembles and Pólya frequency functions ⋮ Outliers in the spectrum for products of independent random matrices ⋮ On the almost‐circular symplectic induced Ginibre ensemble ⋮ Disk counting statistics near hard edges of random normal matrices: the multi-component regime ⋮ Large gap asymptotics on annuli in the random normal matrix model ⋮ The forbidden region for random zeros: Appearance of quadrature domains ⋮ Exponential moments for disk counting statistics at the hard edge of random normal matrices ⋮ Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits ⋮ Time-inhomogeneous random Markov chains ⋮ A note on the limiting mean distribution of singular values for products of two Wishart random matrices ⋮ Order statistics of the moduli of the eigenvalues of product random matrices from polynomial ensembles ⋮ Products of independent elliptic random matrices ⋮ Gaussian fluctuations for linear eigenvalue statistics of products of independent iid random matrices ⋮ Universality of the number variance in rotational invariant two-dimensional Coulomb gases

Uses Software

• DLMF

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