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Accelerating Langevin Dynamics with Weighted Laplacian Flow: Global Well-Posedness and Exponential Convergence
We study an accelerated Langevin equation in which the classical overdamped Langevin drift is supplemented by a nonlocal gradient velocity determined through a target-weighted Poisson equation. The target $p$ is only assumed to be strictly positive and need not be normalized. Writing the dynamics in
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