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.

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