Large deviations for the largest eigenvalue of an Hermitian Brownian   motion
  We establish a large deviation principle for the process of the largest eigenvalue of an Hermitian Brownian motion. By a contraction principle, we recover the LDP for the largest eigenvalue of a rank one deformation of the GUE. 
Catherine Donati-Martin (LPMA), Myl\`ene Ma\"ida (LM-Orsay)
math.PR