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This review treats the mathematical and algorithmic foundations of non-reversible Markov chains in the context of event-chain Monte Carlo (ECMC), a continuous-time lifted Markov chain that employs the factorized Metropolis algorithm. It analyzes a number of model applications, and then reviews the formulation as well as the performance of ECMC in key models in statistical physics. Finally, the review reports on an ongoing initiative to apply the method to the sampling problem in molecular simulation, that is, to real-world models of peptides, proteins, and polymers in aqueous solution.
We study the dynamics of one-dimensional (1D) interacting particles simulated with the event-chain Monte Carlo algorithm (ECMC). We argue that previou
We apply the event-chain Monte Carlo algorithm to classical continuum spin models on a lattice and clarify the condition for its validity. In the two-dimensional XY model, it outperforms the local Monte Carlo algorithm by two orders of magnitude, alt
We present a multithreaded event-chain Monte Carlo algorithm (ECMC) for hard spheres. Threads synchronize at infrequent breakpoints and otherwise scan for local horizon violations. Using a mapping onto absorbing Markov chains, we rigorously prove the
We generalize the rejection-free event-chain Monte Carlo algorithm from many particle systems with pairwise interactions to systems with arbitrary three- or many-particle interactions. We introduce generalized lifting probabilities between particles
We discuss prospects for Monte Carlo event generators incorporating the dynamics of transverse momentum dependent (TMD) parton distribution functions. We illustrate TMD evolution in the parton branching formalism, and present Monte Carlo applications of the method.