Workshop Industrial equipment, Tools, Electronics Extreme Value Theory for Particle Systems with Nikos Kolliopoulos 2023

We develop an Extreme Value Theory for a specific type of diffusive particle systems with mean-field interaction in drifts. When the number of particles increases, the upper order statistics of the system converge to the same limit as independent copies of the solution to the corresponding McKean-Vlasov SDE. By utilizing standard Extreme Value Theory and Malliavin Calculus, we can describe this limit. We find that if certain growth conditions are met, the normalized top-ranked particle will follow a Gumbel law in the limit of a large population.