Softcover ISBN:  9780821843734 
Product Code:  ULECT/51 
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eBook ISBN:  9781470416461 
Product Code:  ULECT/51.E 
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AMS Member Price:  $52.00 
Softcover ISBN:  9780821843734 
eBook: ISBN:  9781470416461 
Product Code:  ULECT/51.B 
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AMS Member Price:  $107.20 $81.20 
Softcover ISBN:  9780821843734 
Product Code:  ULECT/51 
List Price:  $69.00 
MAA Member Price:  $62.10 
AMS Member Price:  $55.20 
eBook ISBN:  9781470416461 
Product Code:  ULECT/51.E 
List Price:  $65.00 
MAA Member Price:  $58.50 
AMS Member Price:  $52.00 
Softcover ISBN:  9780821843734 
eBook ISBN:  9781470416461 
Product Code:  ULECT/51.B 
List Price:  $134.00 $101.50 
MAA Member Price:  $120.60 $91.35 
AMS Member Price:  $107.20 $81.20 

Book DetailsUniversity Lecture SeriesVolume: 51; 2009; 154 ppMSC: Primary 60; 30; 15
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 “pointrepulsion”, 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 IASPark City Summer School in 2007; the only background knowledge assumed can be acquired in firstyear graduate courses in analysis and probability.
ReadershipGraduate students and research mathematicians interested in random processes and their relations to complex analysis.

Table of Contents

Chapters

Chapter 1. Introduction

Chapter 2. Gaussian analytic functions

Chapter 3. Joint intensities

Chapter 4. Determinantal point processes

Chapter 5. The hyperbolic GAF

Chapter 6. A determinantal zoo

Chapter 7. Large deviations for zeros

Chapter 8. Advanced topics: Dynamics and allocation to random zeros


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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 “pointrepulsion”, 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 IASPark City Summer School in 2007; the only background knowledge assumed can be acquired in firstyear graduate courses in analysis and probability.
Graduate students and research mathematicians interested in random processes and their relations to complex analysis.

Chapters

Chapter 1. Introduction

Chapter 2. Gaussian analytic functions

Chapter 3. Joint intensities

Chapter 4. Determinantal point processes

Chapter 5. The hyperbolic GAF

Chapter 6. A determinantal zoo

Chapter 7. Large deviations for zeros

Chapter 8. Advanced topics: Dynamics and allocation to random zeros