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]
  2. C. Cammarota, Decay of correlations for infinite range interactions in unbounded spin systems. Comm. Math. Phys. 85 (1982) 517–528. [CrossRef] [MathSciNet]
  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]
  4. A. Chatterjee, M. Katsoulakis and D. Vlachos, Spatially adaptive grand canonical ensemble Monte Carlo simulations. Phys. Rev. E 71 (2005) 026702. [CrossRef]
  5. T.M. Cover and J.A. Thomas, Elements of Information Theory. John Wiley and Sons, Inc. (1991).
  6. G.A. Gallavotti and S. Miracle-Sole, Correlation functions of a lattice system. Comm. Math. Phys. 7 (1968) 274–288. [CrossRef] [MathSciNet]
  7. N. Goldenfeld, Lectures on Phase Transitions and the Renormalization Group, Volume 85. Addison-Wesley, New York (1992).
  8. C. Gruber and H. Kunz, General properties of polymer systems. Comm. Math. Phys. 22 (1971) 133–161. [CrossRef] [MathSciNet]
  9. M. Hildebrand and A.S. Mikhailov, Mesoscopic modeling in the kinetic theory of adsorbates. J. Chem. Phys. 100 (1996) 19089. [CrossRef]
  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]
  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]
  12. L. Kadanoff, Scaling laws for Ising models near tc. Physics 2 (1966) 263.
  13. M. Katsoulakis and J. Trashorras, Information loss in coarse-graining of stochastic particle dynamics. J. Statist. Phys. 122 (2006) 115–135. [CrossRef]
  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]
  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]
  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).
  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]
  18. D.A. Lavis and G.M. Bell, Statistical Mechanics of Lattice Systems, Volume I. Springer Verlag (1999).
  19. J.E. Mayer, Integral equations between distribution functions of molecules. J. Chem. Phys. 15 (1947) 187–201. [CrossRef]
  20. R. Peierls, On Ising's model of ferromagnetism. Proc. Camb. Philos. Soc. 32 (1936) 477–481. [CrossRef]
  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]
  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]
  23. B. Simon, The Statistical Mechanics of Lattice Gases, Vol. I. Princeton series in Physics (1993).
  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]
  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. [CrossRef] [MathSciNet]

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