Free Access
Volume 41, Number 3, May-June 2007
Page(s) 627 - 660
Published online 02 August 2007
  1. J. Bricmont, A. Kupiainen and R. Lefevere, Renormalization group pathologies and the definition of Gibbs states. Comm. Math. Phys. 194 (1998) 359–388. [CrossRef] [MathSciNet] [Google Scholar]
  2. C. Cammarota, Decay of correlations for infinite range interactions in unbounded spin systems. Comm. Math. Phys. 85 (1982) 517–528. [CrossRef] [MathSciNet] [Google Scholar]
  3. A. Chatterjee, M. Katsoulakis and D. Vlachos, Spatially adaptive lattice coarse-grained Monte Carlo simulations for diffusion of interacting molecules. J. Chem. Phys. 121 (2004) 11420–11431. [CrossRef] [PubMed] [Google Scholar]
  4. A. Chatterjee, M. Katsoulakis and D. Vlachos, Spatially adaptive grand canonical ensemble Monte Carlo simulations. Phys. Rev. E 71 (2005) 026702. [CrossRef] [Google Scholar]
  5. T.M. Cover and J.A. Thomas, Elements of Information Theory. John Wiley and Sons, Inc. (1991). [Google Scholar]
  6. G.A. Gallavotti and S. Miracle-Sole, Correlation functions of a lattice system. Comm. Math. Phys. 7 (1968) 274–288. [CrossRef] [MathSciNet] [Google Scholar]
  7. N. Goldenfeld, Lectures on Phase Transitions and the Renormalization Group, Volume 85. Addison-Wesley, New York (1992). [Google Scholar]
  8. C. Gruber and H. Kunz, General properties of polymer systems. Comm. Math. Phys. 22 (1971) 133–161. [Google Scholar]
  9. M. Hildebrand and A.S. Mikhailov, Mesoscopic modeling in the kinetic theory of adsorbates. J. Chem. Phys. 100 (1996) 19089. [Google Scholar]
  10. A.E. Ismail, G.C. Rutledge and G. Stephanopoulos, Multiresolution analysis in statistical mechanics. I. Using wavelets to calculate thermodynamics properties. J. Chem. Phys. 118 (2003) 4414–4424. [CrossRef] [Google Scholar]
  11. A.E. Ismail, G.C. Rutledge and G. Stephanopoulos, Multiresolution analysis in statistical mechanics. II. Wavelet transform as a basis for Monte Carlo simulations on lattices. J. Chem. Phys. 118 (2003) 4424. [CrossRef] [Google Scholar]
  12. L. Kadanoff, Scaling laws for Ising models near tc. Physics 2 (1966) 263. [Google Scholar]
  13. M. Katsoulakis and J. Trashorras, Information loss in coarse-graining of stochastic particle dynamics. J. Statist. Phys. 122 (2006) 115–135. [CrossRef] [Google Scholar]
  14. M. Katsoulakis, A. Majda and D. Vlachos, Coarse-grained stochastic processes for microscopic lattice systems. Proc. Natl. Acad. Sci. 100 (2003) 782–782. [CrossRef] [MathSciNet] [Google Scholar]
  15. M.A. Katsoulakis, A.J. Majda and D.G. Vlachos, Coarse-grained stochastic processes and Monte Carlo simulations in lattice systems. J. Comp. Phys. 186 (2003) 250–278. [CrossRef] [Google Scholar]
  16. M.A. Katsoulakis, P. Plecháč, L. Rey-Bellet and D.K. Tsagkarogiannis, Coarse-graining schemes for lattice systems with short and long range interactions. (In preparation). [Google Scholar]
  17. M.A. Katsoulakis, P. Plecháč and A. Sopasakis, Error analysis of coarse-graining for stochastic lattice dynamics. SIAM J. Numer. Anal. 44 (2006) 2270. [CrossRef] [MathSciNet] [Google Scholar]
  18. D.A. Lavis and G.M. Bell, Statistical Mechanics of Lattice Systems, Volume I. Springer Verlag (1999). [Google Scholar]
  19. J.E. Mayer, Integral equations between distribution functions of molecules. J. Chem. Phys. 15 (1947) 187–201. [CrossRef] [Google Scholar]
  20. R. Peierls, On Ising's model of ferromagnetism. Proc. Camb. Philos. Soc. 32 (1936) 477–481. [Google Scholar]
  21. I.V. Pivkin and G.E. Karniadakis, Coarse-graining limits in open and wall-bounded dissipative particle dynamics systems. J. Chem. Phys. 124 (2006) 184101. [CrossRef] [PubMed] [Google Scholar]
  22. A. Procacci, B.N.B. De Lima and B. Scoppola, A remark on high temperature polymer expansion for lattice systems with infinite range pair interactions. Lett. Math. Phys. 45 (1998) 303–322. [CrossRef] [MathSciNet] [Google Scholar]
  23. B. Simon, The Statistical Mechanics of Lattice Gases, Vol. I. Princeton series in Physics (1993). [Google Scholar]
  24. A. Szepessy, R. Tempone and G.E. Zouraris, Adaptive weak approximation of stochastic differential equations. Comm. Pure Appl. Math. 54 (2001) 1169–1214. [CrossRef] [MathSciNet] [Google Scholar]
  25. A.C.D. van Enter, R. Fernández and A.D. Sokal, Regularity properties and pathologies of position-space renormalization-group transformations: scope and limitations of Gibbsian theory. J. Statist. Phys. 72 (1993) 879–1167. [Google Scholar]

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