**University Lecture Series**

Volume: 51;
2009;
154 pp;
Softcover

MSC: Primary 60; 30; 15;

Print ISBN: 978-0-8218-4373-4

Product Code: ULECT/51

List Price: $41.00

Individual Member Price: $32.80

**Electronic ISBN: 978-1-4704-1646-1
Product Code: ULECT/51.E**

List Price: $41.00

Individual Member Price: $32.80

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#### Supplemental Materials

# Zeros of Gaussian Analytic Functions and Determinantal Point Processes

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*J. Ben Hough; Manjunath Krishnapur; Yuval Peres; Bálint Virág*

The book examines in some depth two important classes of point
processes, determinantal processes and “Gaussian zeros”,
i.e., zeros of random analytic functions with Gaussian
coefficients. These processes share a property of
“point-repulsion”, where distinct points are less likely
to fall close to each other than in processes, such as the Poisson
process, that arise from independent sampling. Nevertheless, the
treatment in the book emphasizes the use of independence: for random
power series, the independence of coefficients is key; for
determinantal processes, the number of points in a domain is a sum of
independent indicators, and this yields a satisfying explanation of
the central limit theorem (CLT) for this point count. Another unifying
theme of the book is invariance of considered point processes under
natural transformation groups.

The book strives for balance between general theory and concrete examples.
On the one hand, it presents a primer on modern techniques on the
interface of probability and analysis. On the other hand, a wealth of
determinantal processes of intrinsic interest are analyzed; these arise
from random spanning trees and eigenvalues of random matrices, as well as
from special power series with determinantal zeros.

The material in the book formed the basis of a graduate course given at
the IAS-Park City Summer School in 2007; the only background knowledge
assumed can be acquired in first-year graduate courses in analysis and
probability.

#### Readership

Graduate students and research mathematicians interested in random processes and their relations to complex analysis.

#### Table of Contents

# Table of Contents

## Zeros of Gaussian Analytic Functions and Determinantal Point Processes

- Cover Cover11 free
- Title page iii4 free
- Contents v6 free
- Preface vii8 free
- Introduction 112 free
- Gaussian analytic functions 1324 free
- Joint intensities 3546
- Determinantal point processes 4758
- The hyperbolic GAF 8394
- A determinantal zoo 99110
- Large deviations for zeros 119130
- Advanced topics: Dynamics and allocation to random zeros 135146
- Bibliography 149160
- Back Cover Back Cover1170