Date:

Wed, 23/06/202112:00-13:00

Location:

Ross, room 70

Title: Gap probability for the product of Ginibre matrices in the critical regime

Abstract:

Consider a product of M independent identically distributed (i.i.d.) complex Gaussian matrices of size NxN with Gaussian i.i.d. entries. Recently, D.-Zh. Liu, D. Wang, and Y. Wang proved that in the critical regime, that is, passing both N and M to infinity in such a way that the ratio M/N converges to a positive constant, the singular values of this product form a determinantal point process. The main focus of the talk is the asymptotic behavior of the corresponding gap probability: We are going to discuss how likely it is to have no points of this newly emerged process in the semi-infinite interval (a, +inf), a>0, if a is large. An explicit asymptotic result will be presented, based on joint work with E. Strahov. No prior knowledge of random matrix theory is required.

Abstract:

Consider a product of M independent identically distributed (i.i.d.) complex Gaussian matrices of size NxN with Gaussian i.i.d. entries. Recently, D.-Zh. Liu, D. Wang, and Y. Wang proved that in the critical regime, that is, passing both N and M to infinity in such a way that the ratio M/N converges to a positive constant, the singular values of this product form a determinantal point process. The main focus of the talk is the asymptotic behavior of the corresponding gap probability: We are going to discuss how likely it is to have no points of this newly emerged process in the semi-infinite interval (a, +inf), a>0, if a is large. An explicit asymptotic result will be presented, based on joint work with E. Strahov. No prior knowledge of random matrix theory is required.