Zeros of Gaussian Analytic Functions

Zeros of Gaussian Analytic Functions and Determinantal Point Processes

Contents Preface vii Chapter 1. Introduction 1 1.1. Random polynomials and their zeros 1 1.2. Basic notions and definitions 6 1.3. Hints and solutions 11 Chapter 2. Gaussian Analytic Functions 13 2.

Zeros of Random Analytic Functions

Zeros of Random Analytic Functions The dominant theme of this thesis is that random matrix valued analytic functions, generalizing both random matrices and random analytic functions, for many purposes can (and perhaps should) be effectively studied in that level of generality. We study zeros of random analytic functions in one complex variable. It is known that there is a one parameter family o...

Gaussian versus Optimal Integration of Analytic Functions

We consider error estimates for optimal and Gaussian quadrature for-mulae if the integrand is analytic and bounded in a certain complex region. First, a simple technique for the derivation of lower bounds for the optimal error constants is presented. This method is applied to Szegg o-type weight functions and ellipses as regions of analyticity. In this situation, the error constants for the Gau...

On locating clusters of zeros of analytic functions

Given an analytic function f and a Jordan curve γ that does not pass through any zero of f , we consider the problem of computing all the zeros of f that lie inside γ, together with their respective multiplicities. Our principal means of obtaining information about the location of these zeros is a certain symmetric bilinear form that can be evaluated via numerical integration along γ. If f has ...

The Calculation of Zeros of Polynomials and Analytic Functions