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. This title presents a primer on modern techniques on the interface of probability and analysis. Series: University Lecture Series. Num Pages: 154 pages, Illustrations. BIC Classification: PBKF. Category: (UP) Postgraduate, Research & Scholarly. Dimension: 262 x 179 x 13. Weight in Grams: 312. . 2009. Paperback. . . . .

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Bibliographic Details

Title: Zeros of Gaussian Analytic Functions and Determinantal Point Processes (University Lecture Series)
Publisher: American Mathematical Society
Publication Date: 2009
Language: English
ISBN 10: 0821843737
ISBN 13: 9780821843734
Binding: Soft cover
Condition: New

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Synopsis

Material presented here formed the basis of a graduate course given at the IAS-Park City Summer School in 2007, offering a primer on modern techniques on the interface of probability and analysis. With chapter exercises and b&w illustrations, the book is appropriate as a text for graduate students in probability, analysis, and mathematical physics. No familiarity with physics is assumed, but readers should have first-year graduate knowledge of analysis and probability. Striving for balance between general theory and concrete examples, the book adopts a probabilistic perspective, stressing the invariance of considered point processes under natural transformation groups. Chapters cover Gaussian analytic functions (GAFs), joint intensities, determinantal point processes, the hyperbolic GAF, a determinantal zoo, and large deviations for zeros. In the final chapter on dynamics and allocation to random zeros, a method is presented by which the zero set of the hyperbolic Gaussian analytic function (GAF) can be made into a time-homogeneous Markov process. The audience for the book is composed of graduate students and research mathematicians interested in random processes and their relationship to complex analysis. Hough is affiliated with HBK Capital Management. There is no subject index. Annotation �2009 Book News, Inc., Portland, OR (booknews.com)

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