Tim Rogers

Spectra of Sparse Non-Hermitian Random Matrices

Sparse non-Hermitian random matrices arise in the study of disordered physical systems with asymmetric local interactions, and have applications ranging from neural networks to ecosystem dynamics. The (often beautiful) eigenvalue spectra of these matrices provide crucial information on system stability and susceptibility, however, their study is greatly complicated by the twin challenges of a lack of symmetry and a sparse interaction structure. In this talk I will show how the spectra of sparse non-Hermitian matrices can be computed using tools from statistical mechanics of disordered systems.