Last edited by Galar
Wednesday, May 13, 2020 | History

4 edition of Zeros of Gaussian analytic functions and determinantal point processes found in the catalog.

# Zeros of Gaussian analytic functions and determinantal point processes

Written in

Subjects:
• Gaussian processes,
• Analytic functions,
• Polynomials,
• Point processes

• Edition Notes

Includes bibliographical references.

Classifications The Physical Object Statement J. Ben Hough ... [et al.]. Series University lecture series -- v. 51 Contributions Hough, J. Ben, 1979- LC Classifications QA274.4 .Z47 2009 Pagination p. cm. Open Library OL23631473M ISBN 10 9780821843734 LC Control Number 2009027984

Zeros of Gaussian analytic functions—invariance and rigidity Yuval Peres MSRI workshop on conformal invariance and statistical mechanics Lecture notes, pm, Ma Notes taken by Samuel S Watson A point process is a random conﬁguration of points in a space such as Rd. Equivalently, a point process is a random discrete measure.   We study a family of random Taylor series \begin{aligned} F(z) = \sum _{n\ge 0} \zeta _n a_n z^n \end{aligned} with radius of convergence almost surely 1 and independent, identically distributed complex Gaussian coefficients $$(\zeta _n)$$ ; these Taylor series are distinguished by the invariance of their zero sets with respect to isometries of the unit by: 2.

IV Zeros of an Analytic Function 1 IV Zeros of an Analytic Function Note. We now explore factoring series in a way analogous to factoring a poly-nomial. Recall that if p is a polynomial with a zero a of multiplicity m, then p(z) = (z − a)mt(z) for a polynomial t(z) such that t(a) 6= 0. Size: 59KB. A notable example is the Gaussian Entire Function, whose zero set is well-known to be invariant with respect to the isometries of the complex plane. We explore the rigidity of the zero set of Gaussian Taylor series, a phenomenon discovered not long ago by Ghosh and Peres for the Gaussian Entire : Avner Kiro, Alon Nishry.

First, we provide the construction of diffusion processes on the space of configurations whose invariant measure is the law of a determinantal point process. Second, we present some algorithms to sample from the law of a determinantal point process on a finite window. Related open problems are by:   Abstract. We show that as n changes, the characteristic polynomial of the n×n random matrix with i.i.d. complex Gaussian entries can be described recursively tCited by: 5.

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### Zeros of Gaussian analytic functions and determinantal point processes Download PDF EPUB FB2

Samples of a translation invariant determinantal pro- cess (left) and zeros of a Gaussian analytic function. Determinantal processes exhibit repulsion at all distances, and the zeros repel at short distances only.

However, the distinction is not evident in the pictures. 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 5/5(1).

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. 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. Zeros of Gaussian Analytic Functions and Determinantal Point Processes About this Title. Ben Hough, HBK Capital Management, New York, NY, Manjunath Krishnapur, Indian Institute of Science, Bangalore, India, Yuval Peres, Microsoft Research, Redmond, WA and Bálint Virág, University of Toronto, Toronto, ON, Canada.

Publication: University Lecture SeriesCited by: 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.

Destination page number Search scope Search Text Search scope Search Text. polynomials and their zeros are a core subject of this book; the other class consists of processes with joint intensities of determinantal form.

The intersection of the two. Chapter 2. Gaussian Analytic Functions 13 Complex Gaussian distribution 13 Gaussian analytic functions 15 Isometry-invariant zero sets 18 Distribution of zeros - The ﬁrst intensity 23 Intensity of zeros determines the GAF 29 Notes 31 Hints and solutions 32 Chapter 3.

Joint Intensities 35 Introduction. We study zeros of random analytic functions in one complex variable. It is known that there is a one parameter family of Gaussian analytic functions with zero sets that are stationary in each of the three symmetric spaces, namely the plane, the sphere and the unit disk, under the corresponding group of by: determinantal processes.

In particular, (3) extends the known fact that p(z 1,z 2) zeros are negatively correlated. In fact, ZU is the only process of zeros of a Gaussian analytic function which is negatively correlated and.

Zeros of Gaussian Analytic Functions and Determinantal Point Processes (University Lecture Series)的话题 (全部 条) 什么是话题 无论是一部作品、一个人，还是一件事，都往往可以衍生出许多不同的话题。.

BibTeX @MISC{Hough_zerosof, author = {John Ben Hough and Manjunath Krishnapur and Yuval Peres and Bálint Virág}, title = {Zeros of Gaussian Analytic Functions and Determinantal Point Processes.

Fractals in Probability and Analysis, by Christopher Bishop and Yuval Peres. Cambridge University Press, ; Brownian motion, by Peter Mörters and Yuval Peres. Cambridge University Press, Zeros of Gaussian Analytic Functions and Determinantal Point Processes, by Ben J. Hough, Manjunath Krishnapur, Balint Virag and Yuval Peres.

by eg for any xed analytic function g. Proving this theorem and some basic properties about the zero set of the planar GAF is the content of the rst two lectures.

We will follow the book Zeros of Gaussian Analytic unctionsF and Determinantal Point Processes by Hough, Krishnapur, Peres and Virag. Zero set of the hyperbolic GAF. Introduction A Gaussian analytic function is a linear combination of analytic functions fk: G — > C (G C C is a domain), \fk (z)\ 2 0 with independent standard complex Gaussian random coefficients Q^.

The random zero set Zf = / _1 (0) is the theme of this talk. Rigidity and tolerance in point processes: Gaussian zeros and Ginibre eigenvalues. Subhroshekhar Ghosh and Yuval Peres “Determinantal point processes” in The Oxford Handbook of Random Matrix Theory, Oxford Univ.

Press, Zeros of Gaussian analytic functions, Math. Res. Lett. 7 (), Cited by: Free 2-day shipping. Buy Zeros of Gaussian Analytic Functions and Determinantal Point Processes at nd: Hough, J. Ben. "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. Get this from a library. Zeros of Gaussian analytic functions and determinantal point processes.

[J Ben Hough;] -- 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. On the other hand, if zeros of a Gaussian entire function F have a translation-invariant distribution, then the mean En F is a translation-invariant measure on C.

Hence, it is proportional to the area measure m; i.e., En F Lmwith a constant L>0. Then by the Calabi rigidity, the zero sets Z F and Z fL have the same distribution.

In other.This year's reading group is on zeros of Gaussian analytic functions (GAF). The first part will deal with Gaussian holomorphic functions on the complex domains, in which case the zero sets are point processes.

The second part deals with Gaussian real analytic functions, mainly from the plane. In this case the zero sets are given by closed curves.Determinantal point process. In mathematics, a determinantal point process is a stochastic point process, the probability distribution of which is characterized as a determinant of some function.

Such processes arise as important tools in random matrix theory, combinatorics, physics, and wireless network modeling.