Seminar series
          
      Date
              Tue, 21 Oct 2025
      
      
          Time
        14:00 - 
        15:00
          Location
              L3
          Speaker
              Prof Panagiotis E. Souganidis 
          Organisation
              University of Chicago
          Using novel arguments as well as techniques developed over the last  twenty years to study mean field games, in this paper (i) we investigate the optimal control of the Dyson equation, which is the mean field equation for the so-called Dyson Brownian motion, that is, the stochastic particle system satisfied by the eigenvalues of large random matrices, (ii) we establish the well-posedness of the resulting infinite dimensional Hamilton-Jacobi equation, 
(iii) we provide a complete and direct proof for the large deviations for the spectrum of large random matrices, and (iv) we study the asymptotic behavior of the transition probabilities of the Dyson Brownian motion.  Joint work with Charles Bertucci and Pierre-Louis Lions.
 
    