Non-reversible lifts of reversible diffusion processes and relaxation times

Autor:	Eberle, Andreas, Lörler, Francis
Rok vydání:	2024
Předmět:	Mathematics - Probability Mathematics - Analysis of PDEs Mathematics - Numerical Analysis Mathematics - Statistics Theory Statistics - Computation 60J25 60J60 60J35 60H10 65C40
Druh dokumentu:	Working Paper
Popis:	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. Comment: Fixed error in Section 5. 30 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2402.05041 Zobrazit plný text záznamu View this record from Arxiv