Gaussian complex zeros are not always normal

14 Out 2022 - 00:00:00
12:00
Aula seminario de análise matemático, Facultade matemáticas USC

"Gaussian complex zeros are not always normal", impartido por Jeremiah Buckley, King's College London.

Data: 14 de outubro

Hora: 12:00 h.

Lugar:  Aula seminario de análise matemático, Facultade matemáticas USC

Duración: 1 hora

Abstract: 

The “hyperbolic Gaussian analytic function” is a family of random holomorphic functions on the unit disc. It is particularly interesting because the distribution of its zero set is invariant under disc automorphisms. I will discuss the limiting behaviour of the zero set. The family is parameterised by the “intensity”, the mean number of zeroes per unit hyperbolic area. It is known that there is a transition in the behaviour of the variance at a certain value of the intensity, “L=1/2”. Our main finding elaborates on this transition. We will show that for L\ge1/2 the zeroes satisfy a CLT, while for L<1/2 we find a skewed limiting distribution. We will also discuss the case L=0; in this case the “boundary values” of the random function form a “log-correlated process” on the unit circle. Joint work with Alon Nishry (arXiv:2104.12598 [math.PR])

 

Actividade co-financiada coa colaboración da Consellería de Cultura, Educación, Formación Profesional e Universidades