2021/06/17 by François Delarue, Delarue, Francois, William Salkeld +1
Mathematics · Physics and Astronomy · #16T05 #2020 AMS subject classifications: Primary: 60-XX #46G05 #60Lxx Secondary: 60L30 #FOS: Mathematics #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.2106.09801
openalex publication_date 2021/06/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In these notes, we provide an introduction to a new regularity structure used for solving rough mean-field equations. The index set of this regularity structure is described a collection of novel objects which we refer to as Lions trees. These objects arise in Taylor expansions involving the Lions derivative and capture many of the desirable properties of mean-field dynamics. This work represents a comprehensive generalisation of the ideas first introduced in [BCD20] that promise powerful insights into how interactions with a collective determine the dynamics of an individual within this collective.