Essler Krauth 2023
From Werner KRAUTH
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| - | '''F. H. L Essler, W. Krauth''' '''''Lifted TASEP: a Bethe ansatz integrable paradigm for non-reversible Markov chains ''''' ''' Journal of Chemical Physics 156, 084108 (2022)''' | + | '''F. H. L Essler, W. Krauth''' '''''Lifted TASEP: a Bethe ansatz integrable paradigm for non-reversible Markov chains ''''' ''' arXiv:2306.13059 (2023)''' |
| '''Abstract''' | '''Abstract''' | ||
Revision as of 15:19, 18 July 2024
F. H. L Essler, W. Krauth Lifted TASEP: a Bethe ansatz integrable paradigm for non-reversible Markov chains arXiv:2306.13059 (2023)
Abstract Markov-chain Monte Carlo (MCMC), the field of stochastic algorithms built on the concept of sampling, has countless applications in science and technology. The overwhelming majority of MCMC algorithms are time-reversible and thus satisfy the detailed-balance condition, just like physical systems in thermal equilibrium. The underlying Markov chains typically display diffusive dynamics, which leads to a slow exploration of sample space. Significant speedups can be achieved by non-reversible MCMC algorithms exhibiting non-equilibrium dynamics, whose steady states exactly reproduce the target equilibrium states of reversible Markov chains. Such algorithms have had successes in applications but are generally difficult to analyze, resulting in a scarcity of exact results. Here, we introduce the “lifted” TASEP (totally asymmetric simple exclusion process) as a paradigm for non-reversible Markov chains. Our model can be viewed as a second-generation lifting of the reversible Metropolis algorithm on a one-dimensional lattice and is exactly solvable by an unusual kind of coordinate Bethe ansatz. We establish the integrability of the model and present strong evidence that the lifting leads to relaxation on shorter timescales than in the KPZ (Kardar–Parisi–Zhang) universality class.
