Zeros of Gaussian Analytic Functions and Determinantal Point Processes

Silva, C. E.

ISBN 10: 0821843737 / ISBN 13: 9780821843734

Editore: American Mathematical Society, 2009

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Dati bibliografici

• Titolo: Zeros of Gaussian Analytic Functions and Determinantal Point Processes
• Editore: American Mathematical Society
• Data di pubblicazione: 2009
• Lingua: Inglese
• ISBN 10: 0821843737
• ISBN 13: 9780821843734
• Rilegatura: Soft cover
• Disegnatore: Hough, J. Ben; Krishnapur, Manjunath; Peres, Yuval; Virag, Balint
• Condizione: New
• Tipo di libro: Book

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Riassunto

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)