Bernstein theorems and transformations of correlation measures in statistical physics

Kondratiev Y, Chebotarev AM (2006)
MATHEMATICAL NOTES 79(5-6): 649-663.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Kondratiev, YuriUniBi; Chebotarev, AM
Abstract / Bemerkung
We study the class of endomorphisms of the cone of correlation functions generated by probability measures. We consider algebraic properties of the products ((.), star) and the maps K, K-1 which establish relationships between the properties of functions on the configuration space and the properties of the corresponding operators (matrices with Boolean indices): F(gamma) -> (F) over cap (boolean OR)(gamma) = {F(alpha boolean OR beta)}alpha beta subset of gamma. For the operators (F) over cap (boolean OR)(gamma) and (F) over cap (boolean AND)(gamma), we prove conditions which ensure that these operators are positive definite; the conditions are given in terms of complete or absolute monotonicity properties of the function F(gamma).
Stichworte
correlation functions; complete; positivity; Hausdorff space; locally finite measure; K-transform; Lenard theorem; Hibbs measure
Erscheinungsjahr
2006
Zeitschriftentitel
MATHEMATICAL NOTES
Band
79
Ausgabe
5-6
Seite(n)
649-663
ISSN
0001-4346
Page URI
https://pub.uni-bielefeld.de/record/1598773

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Kondratiev Y, Chebotarev AM. Bernstein theorems and transformations of correlation measures in statistical physics. MATHEMATICAL NOTES. 2006;79(5-6):649-663.
Kondratiev, Y., & Chebotarev, A. M. (2006). Bernstein theorems and transformations of correlation measures in statistical physics. MATHEMATICAL NOTES, 79(5-6), 649-663. doi:10.1007/s11006-006-0074-y
Kondratiev, Y., and Chebotarev, A. M. (2006). Bernstein theorems and transformations of correlation measures in statistical physics. MATHEMATICAL NOTES 79, 649-663.
Kondratiev, Y., & Chebotarev, A.M., 2006. Bernstein theorems and transformations of correlation measures in statistical physics. MATHEMATICAL NOTES, 79(5-6), p 649-663.
Y. Kondratiev and A.M. Chebotarev, “Bernstein theorems and transformations of correlation measures in statistical physics”, MATHEMATICAL NOTES, vol. 79, 2006, pp. 649-663.
Kondratiev, Y., Chebotarev, A.M.: Bernstein theorems and transformations of correlation measures in statistical physics. MATHEMATICAL NOTES. 79, 649-663 (2006).
Kondratiev, Yuri, and Chebotarev, AM. “Bernstein theorems and transformations of correlation measures in statistical physics”. MATHEMATICAL NOTES 79.5-6 (2006): 649-663.