Characteristic Polynomials of Non-Symmetric Random Matrices
A talk in the Seminar Zufallsmatrizen series by
Pax Kivimae
| Abstract: | The characteristic polynomials of random matrices have long been studied due their complex behavior, which reflects the behavior of the eigenvalues themselves, and the number of applications they arise in. However, despite considerable work, relatively few results are known about these characteristic polynomials, due to the intractability of computing its statistics in all but the nicest ensembles. In particular, results are primarily known only for symmetric/Hermitian and unitary matrices. In this talk, we discuss work computing the moments of the absolute characteristic polynomial for a particular family of non-symmetric matrix ensembles, namely the real elliptic ensemble. This family includes the real Ginibre ensemble, where our result extends known computations of even moments. Traditionally these computations employ a super-symmetric or combinatorial method, while our method is based on a relation between correlations of characteristic polynomials and the correlation functions of larger matrices, a which makes treatment of the odd absolute moments tenable. Within the CRC this talk is associated to the project(s): C6 |