  For algorithms based on interacting particle systems that admit a mean-field
description, convergence analysis is often more accessible at the mean-field
level. In order to transpose convergence results obtained at the mean-field
level to the finite ensemble size setting, it is desirable to show that the
particle dynamics converge in an appropriate sense to the corresponding
mean-field dynamics. In this paper, we prove quantitative mean-field limit
results for two related interacting particle systems: Consensus-Based
Optimization and Consensus-Based Sampling. Our approach extends Sznitman's
classical argument: in order to circumvent issues related to the lack of global
Lipschitz continuity of the coefficients, we discard an event of small
probability, the contribution of which is controlled using moment estimates for
the particle systems.
