Probability and Mathematical Physics Seminar

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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.