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Coupled coarse graining and Markov Chain Monte Carlo for lattice systems
Mathematics and Statistics Department Faculty Publication Series
  • E Kalligiannaki
  • MA Katsoulakis, University of Massachusetts - Amherst
  • P Plechac
Publication Date
2010
Abstract
We propose an efficient Markov Chain Monte Carlo method for samplingequilibrium distributions for stochastic lattice models, capable of handling correctlylong and short-range particle interactions. The proposed method is a Metropolistypealgorithm with the proposal probability transition matrix based on the coarsegrainedapproximating measures introduced in [17, 21]. We prove that the proposedalgorithm reduces the computational cost due to energy differences and has comparablemixing properties with the classical microscopic Metropolis algorithm, controlledby the level of coarsening and reconstruction procedure. The properties andeffectiveness of the algorithm are demonstrated with an exactly solvable exampleof a one dimensional Ising-type model, comparing efficiency of the single spin-flipMetropolis dynamics and the proposed coupled Metropolis algorithm.
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This is the pre-published version harvested from ArXiv.

Citation Information
E Kalligiannaki, MA Katsoulakis and P Plechac. "Coupled coarse graining and Markov Chain Monte Carlo for lattice systems" (2010)
Available at: http://works.bepress.com/markos_katsoulakis/32/