arXiv subjects

Alexei M. Veneziani

Publications and source records attributed to Alexei M. Veneziani.

3 recordsLinked to original sources

arXiv2011

Asymptotic Integral Kernel for Ensembles of Random Normal Matrix with Radial Potentials

We use the steepest descents method to study the integral kernel of a family of normal random matrix ensembles with eigenvalue distribution P_{N}(z_{1},...,z_{N}) = Z_{N}^{-1} e^{-NΣ_{i=1}^{N}V_α(z_{i})} Π_{1\leqi<j\leqN}|z_{i}-z_{j}|^{2} where V_α(z)=|z|^α, z \in C and α\in ]0,\infty[. Asymptotic analysis with error estimates are obtained. A corollary of this expansion is a scaling limit for the n-point function in terms of the integral kernel for the classical Segal--Bargmann space.

math-ph↗

arXiv2009

Conformal Universality in Normal Matrix Ensembles

A remarkable property of Hermitian ensembles is their universal behavior, that is, once properly rescaled the eigenvalue statistics does not depend on particularities of the ensemble. Recently, normal matrix ensembles have attracted increasing attention, however, questions on universality for these ensembles still remain under debate. We analyze the universality properties of random normal ensembles. We show that the concept of universality used for Hermitian ensembles cannot be directly extrapolated to normal ensembles. Moreover, we show that the eigenvalue statistics of random normal matrices with radially symmetric potential can be made universal under a conformal transformation.

math-ph↗

arXiv2009

Conformal Deformation from Normal to Hermitian Random Matrix Ensembles

We investigate the eigenvalues statistics of ensembles of normal random matrices when their order N tends to infinite. In the model the eigenvalues have uniform density within a region determined by a simple analytic polynomial curve. We study the conformal deformations of normal random ensembles to Hermitian random ensembles and give sufficient conditions for the latter to be a Wigner ensemble.

math.PR↗