Repulsive Mean-Field Couplings and Self-Consistent Transfer Operators

Roberto Castorrini; Stefano Galatolo; Matteo Tanzi

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arXiv · 2609.28664

Repulsive Mean-Field Couplings and Self-Consistent Transfer Operators

Roberto Castorrini·Stefano Galatolo·Matteo Tanzi

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Abstract

We study a one-dimensional self-consistent transfer operator generated by a repulsive mean-field coupling. The interaction admits a natural interpretation as a myopic relocation dynamics balancing congestion and uniformly distributed resources. Using the quantile representation of probability measures, combined with self-consistent transfer operators methods, we prove the existence and uniqueness of a physically relevant invariant measure for the system and characterize it explicitly through a nonlinear fixed-point equation. We then show that the corresponding finite-particle equilibrium converges to the continuum equilibrium with optimal order in Wasserstein distance and establish a quantitative thermodynamic limit.

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Roberto Castorrini, Stefano Galatolo, Matteo Tanzi. 2026-09-23. Repulsive Mean-Field Couplings and Self-Consistent Transfer Operators. https://arxiv.org/abs/2609.28664

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