GIBBS RANDOM FIELDS WITH UNBOUNDED SPINS ON UNBOUNDED DEGREE GRAPHS

Kondratiev Y, Kozitsky Y, Pasurek T (2010)
JOURNAL OF APPLIED PROBABILITY 47(3): 856-875.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Abstract / Bemerkung
Gibbs fields are constructed and studied which correspond to systems of real-valued spins (e.g. systems of interacting anharmonic oscillators) indexed by the vertices of unbounded degree graphs of a certain type, for which the Gaussian Gibbs fields need not be existing. In these graphs, the vertex degree growth is controlled by a summability requirement formulated with the help of a generalized Randic index. In particular, it is proven that the Gibbs fields obey uniform integrability estimates, which are then used in the study of the topological properties of the set of Gibbs fields. In the second part, a class of graphs is introduced in which the mentioned summability is obtained by assuming that the vertices of large degree are located at large distances from each other. This is a stronger version of the metric property employed in Bassalygo and Dobrushin (1986).
Stichworte
Generalized Randie index; Gibbs measure; unbounded; Gibbs specification; spin; unbounded degree graph; DLR equation
Erscheinungsjahr
2010
Zeitschriftentitel
JOURNAL OF APPLIED PROBABILITY
Band
47
Ausgabe
3
Seite(n)
856-875
ISSN
0021-9002
Page URI
https://pub.uni-bielefeld.de/record/1929688

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Kondratiev Y, Kozitsky Y, Pasurek T. GIBBS RANDOM FIELDS WITH UNBOUNDED SPINS ON UNBOUNDED DEGREE GRAPHS. JOURNAL OF APPLIED PROBABILITY. 2010;47(3):856-875.
Kondratiev, Y., Kozitsky, Y., & Pasurek, T. (2010). GIBBS RANDOM FIELDS WITH UNBOUNDED SPINS ON UNBOUNDED DEGREE GRAPHS. JOURNAL OF APPLIED PROBABILITY, 47(3), 856-875. https://doi.org/10.1239/jap/1285335414
Kondratiev, Y., Kozitsky, Y., and Pasurek, T. (2010). GIBBS RANDOM FIELDS WITH UNBOUNDED SPINS ON UNBOUNDED DEGREE GRAPHS. JOURNAL OF APPLIED PROBABILITY 47, 856-875.
Kondratiev, Y., Kozitsky, Y., & Pasurek, T., 2010. GIBBS RANDOM FIELDS WITH UNBOUNDED SPINS ON UNBOUNDED DEGREE GRAPHS. JOURNAL OF APPLIED PROBABILITY, 47(3), p 856-875.
Y. Kondratiev, Y. Kozitsky, and T. Pasurek, “GIBBS RANDOM FIELDS WITH UNBOUNDED SPINS ON UNBOUNDED DEGREE GRAPHS”, JOURNAL OF APPLIED PROBABILITY, vol. 47, 2010, pp. 856-875.
Kondratiev, Y., Kozitsky, Y., Pasurek, T.: GIBBS RANDOM FIELDS WITH UNBOUNDED SPINS ON UNBOUNDED DEGREE GRAPHS. JOURNAL OF APPLIED PROBABILITY. 47, 856-875 (2010).
Kondratiev, Yuri, Kozitsky, Yuri, and Pasurek, Tatiana. “GIBBS RANDOM FIELDS WITH UNBOUNDED SPINS ON UNBOUNDED DEGREE GRAPHS”. JOURNAL OF APPLIED PROBABILITY 47.3 (2010): 856-875.

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