Abstract:We establish a dimension-free, uniform-in-time reverse transportation inequality for Langevin dynamics with non-convex potentials. This inequality controls the Rényi divergence of arbitrary order between the process distributions starting from distinct initial points and serves as the dual version of the Harnack inequality. Notably, we prove that this inequality retains exponential decay in the long-time regime, thereby extending existing results for log-concave sampling to the non-convex setting.
| Subjects: | Probability (math.PR) |
| MSC classes: | 60H10, 62D05, 37A25 |
| Cite as: | arXiv:2512.18598 [math.PR] |
| (or arXiv:2512.18598v2 [math.PR] for this version) | |
| https://doi.org/10.48550/arXiv.2512.18598 arXiv-issued DOI via DataCite |
From: Yuliang Wang [view email]
[v1]
Sun, 21 Dec 2025 05:10:01 UTC (36 KB)
[v2]
Thu, 21 May 2026 18:21:50 UTC (42 KB)
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