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Deterministic Equations for Stochastic Spatial Evolutionary Games
Mathematics and Statistics Department Faculty Publication Series
  • SH Hwang, University of Massachusetts - Amherst
  • MA Katsoulakis, University of Massachusetts - Amherst
  • L Rey-Bellet, University of Massachusetts - Amherst
Publication Date
2010
Abstract
In this paper we investigate the approximation properties of the coarse-graining procedure applied to kinetic Monte Carlo simulations of lattice stochastic dynamics. We provide both analytical and numerical evidence that the hierarchy of the coarse models is built in a systematic way that allows for error control in both transient and long-time simulations. We demonstrate that the numerical accuracy of the CGMC algorithm as an approximation of stochastic lattice spin flip dynamics is of order two in terms of the coarse-graining ratio and that the natural small parameter is the coarse-graining ratio over the range of particle/particle interactions. The error estimate is shown to hold in the weak convergence sense. We employ the derived analytical results to guide CGMC algorithms and we demonstrate a CPU speed-up in demanding computational regimes that involve nucleation, phase transitions and metastability.
Comments

This is the pre-published version harvested from ArXiv.

Citation Information
SH Hwang, MA Katsoulakis and L Rey-Bellet. "Deterministic Equations for Stochastic Spatial Evolutionary Games" (2010)
Available at: http://works.bepress.com/luc_rey_bellet/13/