Alice Guionnet

Large deviations for the largest eigenvalue of random matrices

The understanding of the typical behaviour as well as the fluctuations of the spectrum has made tremendous progresses during the last thirty years. Yet, the study of large deviations has been so far restricted to integrable cases where the joint law of the eigenvalues is explicit or to ''heavy tails'' cases where large deviations are created by large entries. In this talk I will discuss the large deviations of the largest eigenvalue in the case of sub-Gaussian entries. This talk is based on joint works with F. Augeri, N. Cook, R. Ducatez and J. Husson.