Scaling limits of Smoluchowski particles
Probability
2026-03-30 v1
Abstract
We prove a law of large numbers and a functional central limit theorem for the empirical density of a Marcus-Lushnikov model. The limiting density turns out to be the solution of a Smoluchowski equation, and the fluctuations around this limit are shown to be described by an Ornstein-Uhlenbeck process with drift term given by the linearization of the Smoluchowski operator.
Keywords
Cite
@article{arxiv.2603.25868,
title = {Scaling limits of Smoluchowski particles},
author = {Julian Amorim and Arturo Arellano and Milton Jara},
journal= {arXiv preprint arXiv:2603.25868},
year = {2026}
}
Comments
19 pages