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RandomZeroSets SIGNED

Zero sets of random functions

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EC-Contrib. €

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Project "RandomZeroSets" data sheet

The following table provides information about the project.

Coordinator
TEL AVIV UNIVERSITY 

Organization address
address: RAMAT AVIV
city: TEL AVIV
postcode: 69978
website: http://www.tau.ac.il/

contact info
title: n.a.
name: n.a.
surname: n.a.
function: n.a.
email: n.a.
telephone: n.a.
fax: n.a.

 Coordinator Country Israel [IL]
 Total cost 1˙658˙750 €
 EC max contribution 1˙658˙750 € (100%)
 Programme 1. H2020-EU.1.1. (EXCELLENT SCIENCE - European Research Council (ERC))
 Code Call ERC-2015-AdG
 Funding Scheme ERC-ADG
 Starting year 2016
 Duration (year-month-day) from 2016-10-01   to  2021-09-30

 Partnership

Take a look of project's partnership.

# participants  country  role  EC contrib. [€] 
1    TEL AVIV UNIVERSITY IL (TEL AVIV) coordinator 1˙658˙750.00

Map

 Project objective

'The proposed research is focused on zero sets of random functions. This is a rapidly growing area that lies at the crossroads of analysis, probability theory and mathematical physics. Various instances of zero sets of random functions have been used to model different phenomena in quantum chaos, complex analysis, real algebraic geometry, and theory of random point processes.

The proposal consists of three parts. The first one deals with asymptotic topology of zero sets of smooth random functions of several real variables. This can be viewed as a statistical counterpart of the first half of Hilbert's 16th problem. At the same time, it is closely related to percolation theory.

In the second and third parts, we turn to zero sets of random analytic functions of one complex variable. The zero sets studied in the second part provide one of few natural instances of a homogeneous point process with suppressed fluctuations and strong short-range interactions. These point processes have many features, which are in striking contrast with the ones of the Poisson point process. One of these features is the coexistence of different Gaussian scaling limits for different linear statistics.

The third part deals with zeroes of Taylor series with random and pseudo-random coefficients. Studying these zero sets should shed light on the relation between the distribution of coefficients of a Taylor series and the distribution of its zeroes, which is still 'terra incognita' of classical complex analysis.'

 Publications

year authors and title journal last update
List of publications.
2018 Alexander Borichev, Mikhail Sodin, Benjamin Weiss
Spectra of stationary processes on Z
published pages: , ISSN: , DOI:
50 Years with Hardy Spaces A Tribute to Victor Havin 2019-06-13
2018 Alexander Logunov
Nodal sets of Laplace eigenfunctions: polynomial upper estimates of the Hausdorff measure
published pages: 221-239, ISSN: 0003-486X, DOI: 10.4007/annals.2018.187.1.4
Annals of Mathematics 187/1 2019-06-07
2018 Alexander Logunov
Nodal sets of Laplace eigenfunctions: proof of Nadirashvili\'s conjecture and of the lower bound in Yau\'s conjecture
published pages: 241-262, ISSN: 0003-486X, DOI: 10.4007/annals.2018.187.1.5
Annals of Mathematics 187/1 2019-06-06
2019 Adi Glücksam
Measurably entire functions and their growth
published pages: 307-339, ISSN: 0021-2172, DOI: 10.1007/s11856-018-1800-3
Israel Journal of Mathematics 229/1 2019-06-06

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