Seminario de Sistemas Estocásticos

El Departamento de Matemáticas del Cinvestav-IPN los invita al Seminario de Sistemas Estocásticos. Este seminario se lleva a cabo cada miércoles a las 11:30 hrs, en el salón 238 del Departamento de Matemáticas, Cinvestav-IPN.

§ Biorthogonal ensembles and triangular matrices

9 de diciembre de 2020, 11:30 hrs. Vía ZOOM ID 332 926 9130

Dimitris Cheliotis
University of Athens

Resumen: We will discuss the singular values of certain triangular random matrices. When their elements are i.i.d. standard complex Gaussian random variables, the squares of the singular values form a biorthogonal ensemble, and with an appropriate change in the distribution of the diagonal elements, they give the biorthogonal Laguerre ensemble. For triangular Wigner matrices, we show that the empirical distribution of the appropriately rescaled squares of the singular eigenvalues converge to a distribution with support [0, e], while the rescaled largest singular eigenvalue converges to the square root of e under the additional assumption of mean zero and finite fourth moment for the law of the matrix elements.