Polat Erzincanlı

Polat Erzincanlı is a Research Fellow at the Institute for Advanced Dynamic Uncertainty, where his work develops the mathematical connections between kinetic theory — the branch of theoretical physics concerned with the collective behaviour of large interacting particle systems — and the theory of mean field games. He holds a PhD in Physics from Boğaziçi University (Department of Physics), where his doctoral research examined the derivation of kinetic equations from the BBGKY hierarchy: the chain of coupled evolution equations for the n-particle distribution functions of a classical many-body system, which under a mean-field scaling collapses to the Vlasov equation governing the one-particle distribution. His thesis established quantitative convergence rates for this derivation under mixed initial conditions, extending classical results of Dobrushin and Braun–Hepp to a class of singular interaction potentials arising in plasma physics and gravitational dynamics, and producing sharp estimates for the distance — in bounded Lipschitz metric — between the empirical measure of the particle system and the solution of the limiting Vlasov equation at any fixed time.

The recognition that drove Erzincanlı toward IADU was mathematical: the Vlasov equation — a nonlinear transport PDE for a probability measure on phase space, self-consistently driven by the mean field generated by that very measure — is structurally identical to the Fokker–Planck equation of a McKean–Vlasov stochastic differential equation, which is in turn the infinite-player limit of a mean field game system. Nash equilibrium in the MFG corresponds, under this identification, to the stationarity condition of a variational problem analogous to the minimum free energy principle in statistical mechanics. To develop this correspondence rigorously, he held a visiting fellowship at the Bogolyubov Institute for Theoretical Physics, NAS Ukraine, in Kyiv — an institute whose founding director formulated the BBGKY hierarchy and whose mathematical physics tradition provided the ideal environment for this line of work. His research at BITP produced the first propagation-of-chaos estimates for McKean–Vlasov systems derived entirely by kinetic theory methods rather than probabilistic coupling, and established a precise dictionary between the physical notion of molecular chaos and the game-theoretic notion of approximate Nash equilibrium in large populations.

At IADU, Erzincanlı applies these frameworks to the derivation and justification of mean field game models arising in sovereign debt dynamics, commodity market coordination, and interbank contagion — settings where a large population of strategic agents interact through an aggregate state variable and the MFG system emerges as the continuum limit of an N-player Nash equilibrium. His research establishes the precise conditions — smoothness of the interaction kernel, regularity of the initial distribution, strength of the mean-field coupling — under which the MFG solution faithfully approximates the strategic outcome of the finite-player game, providing the Institute with a rigorous foundation for the use of MFG methods in policy-relevant quantitative work.