Jonathan Husson

Large deviations for the largest eigenvalue of Kronecker matrices.

In many applications of random matrices (in ecology, spin glasses or machine learning for instance), knowing when the extremal eigenvalues of such matrices are atypical is of paramount importance to understand the qualitative behavior of the system we model. We can reformulate this question using the framework of large deviations and ask for a given model : what are the large deviations of the spectrum ? Though the solution of this problem was initially known only for orthogonal/unitary invariant models (such as GUE/GOE), in the last decade there has been numerous advances in this area for more general random matrices. This talk will be about such an advance for the large deviations of the largest eigenvalue of Kronecker random matrices, that is random matrices defined by block where each block are linear combinations of GOE/GUE matrices (therefore allowing for non-trivial correlations between entries). This talk is based on a joint work with Jana Reker and Alice Guionnet (arXiv:2512.1953).