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Almost Gibbsian versus weakly Gibbsian measures

Author

Listed:
  • Maes, C.
  • Redig, F.
  • Moffaert, A. Van
  • Leuven, K. U.

Abstract

We consider two possible extensions of the standard definition of Gibbs measures for lattice spin systems. When a random field has conditional distributions which are almost surely continuous (almost Gibbsian field), then there is a potential for that field which is almost surely summable (weakly Gibbsian field). This generalizes the standard Kozlov theorems. The converse is not true in general as is illustrated by counterexamples.

Suggested Citation

  • Maes, C. & Redig, F. & Moffaert, A. Van & Leuven, K. U., 1999. "Almost Gibbsian versus weakly Gibbsian measures," Stochastic Processes and their Applications, Elsevier, vol. 79(1), pages 1-15, January.
    • Handle: RePEc:eee:spapps:v:79:y:1999:i:1:p:1-15
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    Cited by:

    1. den Hollander, Frank & Steif, Jeffrey E. & van der Wal, Peter, 2005. "Bad configurations for random walk in random scenery and related subshifts," Stochastic Processes and their Applications, Elsevier, vol. 115(7), pages 1209-1232, July.
    2. Häggström, Olle, 2001. "Coloring percolation clusters at random," Stochastic Processes and their Applications, Elsevier, vol. 96(2), pages 213-242, December.
    3. van Enter, Aernout & Le Ny, Arnaud, 2017. "Decimation of the Dyson–Ising ferromagnet," Stochastic Processes and their Applications, Elsevier, vol. 127(11), pages 3776-3791.
    4. Aernout C. D. Van Enter & Frank Redig & Evgeny Verbitskiy, 2008. "Gibbsian and non‐Gibbsian states at Eurandom," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 62(3), pages 331-344, August.

    More about this item

    Keywords

    Gibbs formalism Non-Gibbsian states;

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