Merzi, Dario
Normal matrix models and orthogonal polynomials for a class of potentials with discrete rotational symmetries [Tesi di dottorato]
SISSA, 2015-10-27T07:14:57Z

In this thesis we are going to study normal random matrix models which generalize naturally the polynomially perturbed Ginibre ensamble, focusing in particular on their eigenvalue distribution and on the asymptotics of the associated orthogonal polynomials. \ The main result we are going to present are the following: egin{itemize} item we describe the explicit derivation of the equilibrium measure for a class of potentials with discrete rotational symmetries, namely of the form [V(z)=|z|^{2n}-t(z^{d}+ ar{z}^{d})qquad n,dinmathbb{N}, dleq2n t>0 .] item We obtain the strong asymptotics for the orthogonal polynomials associated to the weight [ e^{-NV(z)},quad V(z)=|z|^{2s}-t(z^s+ ar{z}^{s}) qquad z in mathbb{C},;sin mathbb{N},quad t>0,] and we will show how the density of their zeroes is related to the eigenvalue distribution of the corresponding matrix model; item We show how the conformal maps used to describe the support of the equilibrium measure for polynomial perturbation of the potential

Dubrovin, Boris
Grava, Tamara
Mathematics


Tesi di dottorato. | Lingua: en. | Paese: | BID: TD16087828