Mathematical Aspects of Collective Dynamics:
Kinetic Description and Fractional Diffusion

Anisotropic interactions in crowd dynamics

Alexander Vladimirsky

Cornell University

I will outline consistency requirements for mean-field-game-type models of crowd dynamics. Anisotropies in pedestrians' speed profiles might arise due to a non-local dependence on crowd density or due to multi-crowd interactions. In the latter case, there are also additional challenges in proving the uniqueness of Nash equilibrium. Time permitting, I will also discuss a related formulation of surveillance-evasion games under uncertainty.