Séminaire hybride à l'Université McGill ou Zoom.

This is the third part of the introduction to Quantum Mean Field Games. In this talk, we focus on the dynamics and the mean-field limit of large-scale interacting quantum systems. To address the intractable N-body Stochastic Master Equation (SME) describing a network of quantum agents, we will introduce the concept of the partial trace as a tool to extract the state of a representative agent from the entangled whole and present Kolokoltsov's Quantum Law of Large Numbers (or propagation of chaos), which proves that the reduced state of any single particle converges to a deterministic limit described by a nonlinear Quantum McKean-Vlasov equation. We will discuss the derivation of this limiting equation and the associated convergence rates.

Biography: Tao Zhang is a Ph.D. student in the Department of Electrical and Computer Engineering at McGill University, supervised by Professors Peter Caines and Aditya Mahajan. His research focuses on mean-field game theory in network systems.