Here are the slides for my mini-course Interacting Particle Systems: Almost sure uniqueness, pathwise duality, and the mean-field limit at the Workshop YEP XVII: "Interacting Particle Systems" (Aug 30 - Sep 3, 2021):
Section 1 Poisson Construction of Interacting Particle Systems
Section 2 Pathwise duality
Section 3 The mean-field limit
Section 4 The cooperative branching process
Section 5 Recursive tree process
Section 6 Frozen percolation
Sections 1-3 are loosely based on Chapters 3, 4, and 6 of my lecture notes A Course in Interacting Particle Systems. Sections 3-6 are moreover based on joint work with Tibor Mach, Balázs Ráth, Anja Sturm, Márton Szőke, and Tamás Terpai. My lectures are scheduled for:
Abstract In this mini-course, I will discuss the almost surely unique construction of interacting particle systems from a graphical representation, pathwise duality, and the mean-field limit. The study of pathwise duals in the mean-field limit naturally leads to recursive tree processes and the question of endogeny. Recursive tree processes also occur naturally in the study of frozen percolation, which is an interacting particle system with long-range dependence to which the standard existence and uniqueness results do not apply and for which the question of almost sure uniqueness turns out to be rather subtle.
Here is a link to the interview I gave for the workshop.