Zero sets of random functions

Información del proyecto

RandomZeroSets

Identificador del acuerdo de subvención: 692616

DOI

10.3030/692616

Proyecto cerrado

Fecha de la firma de la CE 3 Mayo 2016

Fecha de inicio 1 Octubre 2016

Fecha de finalización 30 Septiembre 2023

Financiado con arreglo a

• EXCELLENT SCIENCE - European Research Council (ERC)

Coste total

€ 1 658 750,00

Aportación de la UE

€ 1 658 750,00

Coordinado por

TEL AVIV UNIVERSITY
Israel

Periodic Reporting for period 5 - RandomZeroSets (Zero sets of random functions)

Período documentado: 2022-10-01 hasta 2023-09-30

Resumen del contexto y de los objetivos generales del proyecto

The project is focused on zero sets of random functions. This is a rapidly growing area that pertains to pure mathematics (which is a fundamental science) and lies at the crossroads of analysis, probability theory, and mathematical physics. Various instances of zero sets of random functions have been used to model phenomena in quantum chaos, real algebraic geometry, theory of entire functions, and theory of random point processes. The challenging problems addressed in the proposal connect classical fields of mathematics (analysis, probability theory, mathematical physics, and number theory) with such rapidly developing disciplines as spectral geometry, statistical topology, percolation theory.

Trabajo realizado desde el comienzo del proyecto hasta el final del período abarcado por el informe y los principales resultados hasta la fecha

We have investigated a variety of topics, from zero sets of random spherical harmonic, of discrete harmonic functions and of linear combinations of Laplacian eigenfunctions, to rigidity of random processes, zeroes of Taylor series with random and psuedo-random coefficients,
and measurable entire functions.

Avances que van más allá del estado de la técnica e impacto potencial esperado (incluida la repercusión socioeconómica y las implicaciones sociales más amplias del proyecto hasta la fecha)

Our work led us to answers to several long-standing open problems (e.g. Nadirashavili and Nevai conjectures) and to several quite unexpected discoveries concerning behavior of discrete harmonic functions and of linear combination of Laplace eigenfunctions.

Nodal portrait of a random spherical harmonic of degree 80 (Dmitry Beliaev)

Nodal portrait of a random spherical harmonic of degree 40 (Dimtry Beliaev)