The global fluctuation field of non-exchangeable interacting diffusions converges to the universal mean field SPDE limit under deterministic denseness conditions on the interaction matrix, with a sharp n^{-1/2} threshold.
Quantitative propagation of chaos for non-exchangeable diffusions via first-passage percolation
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abstract
This paper develops a non-asymptotic approach to mean field approximations for systems of $n$ diffusive particles interacting pairwise. The interaction strengths are not identical, making the particle system non-exchangeable. The marginal law of any subset of particles is compared to a suitably chosen product measure, and we find sharp relative entropy estimates between the two. Building upon prior work of the first author in the exchangeable setting, we use a generalized form of the BBGKY hierarchy to derive a hierarchy of differential inequalities for the relative entropies. Our analysis of this complicated hierarchy exploits an unexpected but crucial connection with first-passage percolation, which lets us bound the marginal entropies in terms of expectations of functionals of this percolation process.
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math.PR 2years
2026 2representative citing papers
Quantitative quenched propagation of chaos holds for Langevin spin glass dynamics with non-Gaussian i.i.d. disorder satisfying T2, yielding explicit Wasserstein convergence rates and concentration bounds.
citing papers explorer
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Universal Central Limit Theorem for non-exchangeable interacting diffusions
The global fluctuation field of non-exchangeable interacting diffusions converges to the universal mean field SPDE limit under deterministic denseness conditions on the interaction matrix, with a sharp n^{-1/2} threshold.
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Quantitative propagation of chaos and universality for asymmetric Langevin spin glass dynamics
Quantitative quenched propagation of chaos holds for Langevin spin glass dynamics with non-Gaussian i.i.d. disorder satisfying T2, yielding explicit Wasserstein convergence rates and concentration bounds.