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Mathematics of Computation

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ISSN 1088-6842 (online) ISSN 0025-5718 (print)

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Coarse-graining schemes for stochastic lattice systems with short and long-range interactions
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by Markos A. Katsoulakis, Petr Plecháč, Luc Rey-Bellet and Dimitrios K. Tsagkarogiannis PDF
Math. Comp. 83 (2014), 1757-1793 Request permission


We develop coarse-graining schemes for stochastic many-particle microscopic models with competing short- and long-range interactions on a $d$-dimensional lattice. We focus on the coarse-graining of equilibrium Gibbs states, and by using cluster expansions we analyze the corresponding renormalization group map. We quantify the approximation properties of the coarse-grained terms arising from different types of interactions and present a hierarchy of correction terms. We derive semi-analytical numerical coarse-graining schemes that are accompanied by a posteriori error estimates for lattice systems with short- and long-range interactions.
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Additional Information
  • Markos A. Katsoulakis
  • Affiliation: Department of Mathematics, University of Massachusetts, Amherst, Massachusetts 01003 and Department of Applied Mathematics, University of Crete and Foundation of Research – and — Technology-Hellas, Greece
  • Email:
  • Petr Plecháč
  • Affiliation: Department of Mathematical Sciences, University of Delaware, Newark, Delaware 19716
  • Email:
  • Luc Rey-Bellet
  • Affiliation: Department of Mathematics, University of Massachusetts, Amherst, Massachusetts 01003
  • Email:
  • Dimitrios K. Tsagkarogiannis
  • Affiliation: Hausdorff Center for Mathematics, University of Bonn, D-53115 Bonn, Germany
  • Email:
  • Received by editor(s): March 8, 2010
  • Received by editor(s) in revised form: March 22, 2011, and November 9, 2011
  • Published electronically: March 25, 2014
  • Additional Notes: The research of the first author was supported by the National Science Foundation through grants NSF-DMS-0715125, the CDI -Type II award NSF-CMMI-0835673, and the European Commission FP7-REGPOT-2009-1 project “Archimedes Center for Modeling, Analysis and Computation”
    The research of the second author was partially supported by the National Science Foundation under grant NSF-DMS-0813893 and by the Office of Advanced Scientific Computing Research, U.S. Department of Energy under DE-SC0001340; the work was partly done at the Oak Ridge National Laboratory, which is managed by UT-Battelle, LLC under Contract No. DE-AC05-00OR22725
    The research of the third author was partially supported by grant NSF-DMS-06058
    The research of the fourth author has been supported by a Marie Curie Intra European Fellowship within the 7th European Community Framework Program
  • © Copyright 2014 American Mathematical Society
  • Journal: Math. Comp. 83 (2014), 1757-1793
  • MSC (2010): Primary 65C05, 65C20, 82B20, 82B80, 82-08
  • DOI:
  • MathSciNet review: 3194129