Abstract
We study asymptotics of orthogonal polynomial measures of the form |HN| 2 d∞ where HN are real or complex Hermite polynomials with re- spect to the Gaussian measure ∞. By means of dierential equations on Laplace transforms, interpolation between the (real) arcsine law and the (complex) uniform distribution on the circle is emphasized. Suitable aver- ages by an independent uniform law give rise to the limiting semi-circular and circular laws of Hermitian and non-Hermitian Gaussian random matrix models. The intermediate regime between strong and weak non-Hermiticity is clearly identified on the limiting dierential equation by means of an addi- tional normal variable in the vertical direction.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
