Operator limit of the bulk process

Valkó Benedek előadásának absztraktja

(Joint with Bálint Virág)

2012. július 5. csütörtök, 16:15

 
 

By the Hilbert-Pólya conjecture the critical zeros of the Riemann zeta function correspond to the eigenvalues of a self adjoint operator. By a conjecture of Dyson and Montgomery the critical zeros (after a certain rescaling) look like the bulk eigenvalue limit point process of the Gaussian Unitary Ensemble. It is natural to ask if this point process can be described as the spectrum of a random self adjoint operator. I will show that this is indeed the case: for any β>0 the bulk limit of the Gaussian β ensemble can be obtained as the spectrum of a self adjoint random differential operator. I will describe the operator and show how to derive it as the limit of operators corresponding to finite ensembles in the circular β ensemble case.


 
Balázs Márton, 2012.06.22