A mean-field approach to self-interacting network, convergence and regularity

TL;DR

This paper investigates the behavior of a system of interacting particles modeling filament networks, proving convergence to a mean-field limit and establishing regularity results, with applications to mycelium network formation.

Contribution

It introduces a mean-field framework for self-interacting networks, proving convergence and regularity, and discusses its application to biological filament networks like mycelium.

Findings

Proved convergence of empirical density to mean-field limit.

Established regularity properties of the mean-field solution.

Applied the model to biological networks such as mycelium.

Abstract

The propagation of chaos property for a system of interacting particles, describing the spatial evolution of a network of interacting filaments is studied. The creation of a network of mycelium is analyzed as representative case, and the generality of the modeling choices are discussed. Convergence of the empirical density for the particle system to its mean field limit is proved, and a result of regularity for the solution is presented.