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Zeros of Gaussian Analytic Functions and Determinantal Point Processes
 
J. Ben Hough HBK Capital Management, New York, NY
Manjunath Krishnapur Indian Institute of Science, Bangalore, India
Yuval Peres Microsoft Research, Redmond, WA
Bálint Virág University of Toronto, Toronto, ON, Canada
Zeros of Gaussian Analytic Functions and Determinantal Point Processes
Softcover ISBN:  978-0-8218-4373-4
Product Code:  ULECT/51
List Price: $69.00
MAA Member Price: $62.10
AMS Member Price: $55.20
eBook ISBN:  978-1-4704-1646-1
Product Code:  ULECT/51.E
List Price: $65.00
MAA Member Price: $58.50
AMS Member Price: $52.00
Softcover ISBN:  978-0-8218-4373-4
eBook: ISBN:  978-1-4704-1646-1
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
Zeros of Gaussian Analytic Functions and Determinantal Point Processes
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Zeros of Gaussian Analytic Functions and Determinantal Point Processes
J. Ben Hough HBK Capital Management, New York, NY
Manjunath Krishnapur Indian Institute of Science, Bangalore, India
Yuval Peres Microsoft Research, Redmond, WA
Bálint Virág University of Toronto, Toronto, ON, Canada
Softcover ISBN:  978-0-8218-4373-4
Product Code:  ULECT/51
List Price: $69.00
MAA Member Price: $62.10
AMS Member Price: $55.20
eBook ISBN:  978-1-4704-1646-1
Product Code:  ULECT/51.E
List Price: $65.00
MAA Member Price: $58.50
AMS Member Price: $52.00
Softcover ISBN:  978-0-8218-4373-4
eBook ISBN:  978-1-4704-1646-1
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 Details
     
     
    University Lecture Series
    Volume: 512009; 154 pp
    MSC: 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 “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
     
     
    • 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
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 512009; 154 pp
MSC: 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 “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.

  • 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
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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