Non-reversible lifts of reversible diffusion processes and relaxation times
<|reference_start|>Non-reversible lifts of reversible diffusion processes and relaxation times: We propose a new concept of lifts of reversible diffusion processes and show that various well-known non-reversible Markov processes arising in applications are lifts in this sense of simple reversible diffusions. Furthermore, we introduce a concept of non-asymptotic relaxation times and show that these can at most be reduced by a square root through lifting, generalising a related result in discrete time. Finally, we demonstrate how the recently developed approach to quantitative hypocoercivity based on space-time Poincar\'e inequalities can be rephrased and simplified in the language of lifts and how it can be applied to find optimal lifts.<|reference_end|>
@article{eberle2024non-reversible,
    title={Non-reversible lifts of reversible diffusion processes and relaxation
  times},
    author={Andreas Eberle, Francis L"orler},
    journal={arXiv preprint arXiv:2402.05041},
    year={2024},
    archivePrefix={arXiv},
    eprint={2402.05041},
    primaryClass={math.PR cs.NA math.AP math.NA math.ST stat.CO stat.TH}
}