The scaling limit of a particle system with long-range interaction

TL;DR

This paper investigates the macroscopic behavior of a particle system with long-range interactions, establishing conditions under which its scaling limit converges to a well-posed stochastic PDE, advancing understanding of such systems.

Contribution

It provides new conditions on interaction strength relative to particle distance that ensure the scaling limit is a well-posed stochastic PDE.

Findings

Derived conditions for interaction strength and distance

Proved convergence to stochastic PDE

Characterized the macroscopic behavior of long-range systems

Abstract

We describe the macroscopic behaviour of a particle system with long-range interactions. We describe conditions on the interaction strength in dependency of the distance of the particles, such that the scaling limit of the particle system is a well-posed stochastic PDE.