Hydrodynamic limit for repeated averages on the complete graph

Alberto M. Campos; Tertuliano Franco; Markus Heydenreich; Marcel Schrocke

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arXiv · 2503.19743

Hydrodynamic limit for repeated averages on the complete graph

Alberto M. Campos·Tertuliano Franco·Markus Heydenreich·Marcel Schrocke

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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.

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Alberto M. Campos, Tertuliano Franco, Markus Heydenreich, Marcel Schrocke. 2025-03-25. Hydrodynamic limit for repeated averages on the complete graph. https://arxiv.org/abs/2503.19743

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