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Evangelia Kalligiannaki, Markos A. Katsoulakis, Petr Plechac

Coupled coarse graining and Markov Chain Monte Carlo for lattice systems

We propose an efficient Markov Chain Monte Carlo method for sampling equilibrium distributions for stochastic lattice models, capable of handling correctly long and short-range particle interactions. The proposed method is a Metropolistype algorithm with the proposal probability transition matrix based on the coarsegrained approximating measures introduced in [17, 21]. We prove that the proposed algorithm reduces the computational cost due to energy differences and has comparable mixing properties with the classical microscopic Metropolis algorithm, controlled by the level of coarsening and reconstruction procedure. The properties and effectiveness of the algorithm are demonstrated with an exactly solvable example of a one dimensional Ising-type model, comparing efficiency of the single spin-flip Metropolis dynamics and the proposed coupled Metropolis algorithm.

Bibliographical note:

preprint on arXiv: arXiv: 1006.3781 [math.NA]