Hydrodynamic limit for repeated averages on the complete graph
Probability
2025-03-26 v1
Abstract
We establish a hydrodynamical limit for the averaging process on the complete graph with N vertices, showing that, after a timescale of order N, the empirical distribution of opinions converges to a unique measure. Moreover, if the initial distribution is absolutely continuous concerning the Lebesgue measure, the limiting measure remains absolutely continuous and its density satisfies a non-diffusive differential equation, that resembles the Smoluchowski coagulation equation.
Cite
@article{arxiv.2503.19743,
title = {Hydrodynamic limit for repeated averages on the complete graph},
author = {Alberto M. Campos and Tertuliano Franco and Markus Heydenreich and Marcel Schrocke},
journal= {arXiv preprint arXiv:2503.19743},
year = {2025}
}
Comments
12 pages, 3 figures