Probability and Mathematical Physics Seminar

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Non-reversible lifts of reversible diffusion processes and relaxation times

Speaker: Andreas Eberle, Universität Bonn

Location: Warren Weaver Hall 1302

Date: Friday, October 11, 2024, 11:10 a.m.

Synopsis:

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. 
For example, (kinetic) Langevin dynamics and randomised Hamiltonian 
Monte Carlo are lifts of overdamped Langevin dynamics. 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 Poincaré
inequalities can be rephrased in the language of lifts and how it can be 
applied to find optimal lifts.