The eigenvectors of Gaussian matrices with an external source

Romain Allez, Joël Bun, Jean-Philippe Bouchaud

We consider a diffusive matrix process $(X_t{)}_{t\ge 0}$ defined as $X_t:=A+H_t$ where $A$ is a given deterministic Hermitian matrix and $(H_t{)}_{t\ge 0}$ is a Hermitian Brownian mot…