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Non-reversible lifts of reversible diffusion processes and relaxation times (2402.05041v3)

Published 7 Feb 2024 in math.PR, cs.NA, math.AP, math.NA, math.ST, stat.CO, and stat.TH

Abstract: 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.

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