Reverse Transportation and Harnack Inequalities for Underdamped Langevin in the Non-convex Setting

@misc{habring2026reverse,
  title = {{Reverse Transportation and Harnack Inequalities for Underdamped Langevin in the Non-convex Setting}},
  author = {Andreas Habring and Laurenz Nagler},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.02020},
  eprint = {2611.02020},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.02020},
  note = {CC BY 4.0},
}

TY  - UNPB
TI  - Reverse Transportation and Harnack Inequalities for Underdamped Langevin in the Non-convex Setting
AU  - Andreas Habring
AU  - Laurenz Nagler
PY  - 2026
DA  - 2026/11/01
PB  - arXiv
DO  - 10.48550/arxiv.2611.02020
UR  - https://arxiv.org/abs/2611.02020
AB  - We establish a dimension-free long-time reverse transportation, respectively Harnack inequality for the underdamped Langevin dynamics with non-convex potential. Specifically, we prove that for any two initial points z,z' and P_t the underdamped Langevin semigroup, it holds KL(δ_z P_t|δ_z'P_t) ≤ Ce^−χt|z−z'|(ℛ∨|z−z'|) for all t>δ where δ>0 is arbitrarily small and C=C(δ),ℛ,χ>0 are dimension free constants. In particular, our proof extends recent results which are restricted to either the convex underdamped or the non-convex but overdamped setting.
ER  -