The Dyson Game

Tuesday, March 26, 2019 at 11:50am - 12:55pm

Mark Cerenzia - Princeton University

Random matrix statistics emerge in a broad class of strongly correlated systems, with evidence suggesting they can play a universal role comparable to the one Gaussian and Poisson distributions do classically. Indeed, observational studies have identified these statistics among heavy nucleii, Riemann zeta zeros, pedestrians, land divisions, parked cars, perched birds, and other forms of traffic. Noticing that these latter real-world systems all operate in a decentralized manner, we introduce games that admit Coulomb gas dynamics as a Nash equilibrium and investigate their interesting properties, many of which are atypical, or even new, for the literature on many player games. Most notably in one dimension, there is a nonlocal-to-local transition in the population argument of the N-Nash system of PDEs and a sensitivity of local limit behavior to the chosen model of player information. Besides reviewing these recent results, this talk will also discuss some future research directions based on the many questions these results raise.
Location   Hill 705