Edge scaling limits for a family of non-Hermitian random matrix ensembles
2010 (English)In: Probability theory and related fields, ISSN 0178-8051, E-ISSN 1432-2064, Vol. 147, no 1-2, 241-271 p.Article in journal (Refereed) Published
A family of random matrix ensembles interpolating between the Ginibre ensemble of n x n matrices with iid centered complex Gaussian entries and the Gaussian unitary ensemble (GUE) is considered. The asymptotic spectral distribution in these models is uniform in an ellipse in the complex plane, which collapses to an interval of the real line as the degree of non-Hermiticity diminishes. Scaling limit theorems are proven for the eigenvalue point process at the rightmost edge of the spectrum, and it is shown that a non-trivial transition occurs between Poisson and Airy point process statistics when the ratio of the axes of the supporting ellipse is of order n (-1/3). In this regime, the family of limiting probability distributions of the maximum of the real parts of the eigenvalues interpolates between the Gumbel and Tracy-Widom distributions.
Place, publisher, year, edition, pages
2010. Vol. 147, no 1-2, 241-271 p.
Random matrices; Non-Hermitian; Extremes; Tracy-Widom; Gumbel; Airy; Poisson
IdentifiersURN: urn:nbn:se:kth:diva-8640DOI: 10.1007/s00440-009-0207-9ISI: 000274657400008OAI: oai:DiVA.org:kth-8640DiVA: diva2:14016
QC 201006172008-06-042008-06-042010-07-05Bibliographically approved