Quantitative propagation of chaos and universality for asymmetric Langevin spin glass dynamics

TL;DR

This paper provides quantitative convergence rates for Langevin spin glass dynamics with i.i.d. disorder, extending prior qualitative results to explicit bounds under T2 inequality assumptions.

Contribution

It establishes explicit convergence rates and concentration bounds for the propagation of chaos in asymmetric Langevin spin glasses with non-Gaussian disorder.

Findings

Convergence rates in expected Wasserstein distance are derived.

Quantitative concentration rates for Lipschitz observables are established.

The results apply under the T2 inequality condition for disorder.

Abstract

We obtain quantitative estimates on quenched propagation of chaos for Langevin spin glass dynamics with i.i.d. disorder. Prior work in the case of Gaussian disorder established the qualitative convergence of the law of a single spin to a deterministic McKean-Vlasov limit. We prove convergence rates in expected Wasserstein distance and quantitative concentration rates for Lipschitz observables under the assumption that the disorder satisfies the T2 inequality. The proof uses a coupling argument, together with techniques from concentration of measure, filtering theory, and Malliavin calculus