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This is a Quantitative Study study.

October 1, 2025Open Access

Dynamical mean-field analysis of adaptive Langevin diffusions: Propagation-of-chaos and convergence of the linear response

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Authors

FZFan ZhouZhejiang University JKJin Hwan KoJeju National University BLBruno LoureiroCentre National de la Recherche Scientifique

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Implication

This analysis demonstrates convergence of the empirical distribution of Langevin diffusions in systems with random disorder, indicating potential applications in empirical Bayes learning.

Key Points

The empirical distribution of sample paths converges to a deterministic limit law, highlighting a crucial finding in large system limits.
Propagation-of-chaos results reveal insights into the structure of Langevin diffusions with stochastic interactions, characterized by a new deterministic law.
The method employs dynamical mean-field theory to describe the limiting dynamics through fixed-point equations, facilitating advanced theoretical analysis.
These results are significant for applying empirical Bayes in high-dimensional regression, suggesting broader implications for statistical learning models.

Cite This Study

Zhou et al. (2025) studied this question.

synapsesocial.com/papers/68dd91c7fe798ba2fc498570 https://doi.org/10.48550/arxiv.2504.15556

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Implication

This analysis demonstrates convergence of the empirical distribution of Langevin diffusions in systems with random disorder, indicating potential applications in empirical Bayes learning.

Dynamical mean-field analysis of adaptive Langevin diffusions: Propagation-of-chaos and convergence of the linear response

Discussion

Member takes

Implication

Key Points

Cite This Study

Dynamical mean-field analysis of adaptive Langevin diffusions: Propagation-of-chaos and convergence of the linear response

Discussion

Member takes

Implication

Key Points

Cite This Study

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