Complex Hermite Polynomials: from the Semi-circular Law to the Circular Law
نویسنده
چکیده
We study asymptotics of orthogonal polynomial measures of the form |HN |2dγ where HN are real or complex Hermite polynomials with respect to the Gaussian measure γ. By means of differential equations on Laplace transforms, interpolation between the (real) arcsine law and the (complex) uniform distribution on the circle is emphasized. Suitable averages 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 differential equation by means of an additional normal variable in the vertical direction.
منابع مشابه
Forced Convection Heat Transfer of Non-Newtonian Fluids Through Circular Ducts
The Galerkin finite element method is used to solve the three dimensional continuity, momentum and energy equations for laminar Newtonian and power-law model non-Newtonian flow through horizontal circular tube. The governing equations are non-dimensionalized with respect to specific variables and converted into algebraic equations using appropriate elements. To accelerate convergence a combinat...
متن کاملForced Convection Heat Transfer of Non-Newtonian Fluids Through Circular Ducts
The Galerkin finite element method is used to solve the three dimensional continuity, momentum and energy equations for laminar Newtonian and power-law model non-Newtonian flow through horizontal circular tube. The governing equations are non-dimensionalized with respect to specific variables and converted into algebraic equations using appropriate elements. To accelerate convergence a combinat...
متن کاملImproved Estimates of Kinematic Wave Parameters for Circular Channels
The momentum equation in the kinematic wave model is a power-law equation with two parameters. These parameters, which relate the discharge to the flow area, are commonly derived using Manning’s equation. In general, the values of these parameters depend on the flow depth except for some special cross sections. In this paper, improved estimates of the kinematic wave parameters for circular chan...
متن کاملApplying Differential Transform Method on the Effect of the Elastic Foundation on the out - Plane Displacement of the Functionally Graded Circular Plates
In this paper, the effect of elastic foundation on the out of plane displacement of functionally graded circular plates using differential transform method is presented. Differential transform method is a semi-analytical-numerical solution technique that is capable to solve various types of differential equations. Using this method, governing differential equations are transformed into recursiv...
متن کاملAround the circular law
These expository notes are centered around the circular law theorem, which states that the empirical spectral distribution of a n×n random matrix with i.i.d. entries of variance 1/n tends to the uniform law on the unit disc of the complex plane as the dimension n tends to infinity. This phenomenon is the non-Hermitian counterpart of the semi circular limit for Wigner random Hermitian matrices, ...
متن کامل