Interacting particle systems have numerous applications in statistical
physics, biological modeling, optimization algorithms, and filtering,
among others. For systems exhibiting a mean-field structure, the scaling
limit is commonly referred to as the "propagation of chaos," a concept
introduced in the foundational works of Boltzmann.
For such systems with regular coefficients, I will present a
particularly simple method for computing the limit. This method,
originating from Tanaka (1984), offers an intuitive way to represent
high-dimensional systems by drawing an analogy to ordinary differential
equations (ODEs), focusing on characteristic curves rather than the
underlying partial differential equations (PDEs). In the case of systems
with additive noise, the computation of fluctuations and large
deviations follows straightforwardly. By using an appropriate
discretization, I will also demonstrate how these results can be
extended to systems with multiplicative noise and more general types of
interactions.