Abstract
We introduce Skorohod type integral operators that satisfy an integration by parts formula under Gibbs measures and obtain a characterization of grand canonical Gibbs measures by duality, without use of a differential structure on the underlying configuration space.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Albeverio, S., Kondratiev, Yu G. and Röckner, M.: 'Analysis and geometry on configuration spaces', J. Funct. Anal. 154(2) (1998), 444-500.
Albeverio, S., Kondratiev, Yu.G. and Röckner, M.: 'Analysis and geometry on configuration spaces: The Gibbsian case', J. Funct. Anal. 157(1) (1998), 242-291.
Bouleau, N.: 'Constructions of Dirichlet structures', in: J. Kral et al. (eds), Potential Theory -ICPT' 94, Kouty, Czech Republic, August 13-20, 1994, de Gruyter (1996), 9-25.
da Silva, J.L., Kondratiev, Yu.G. and Röckner, M.: On a Relation between Intrinsic and Extrinsic Dirichlet Forms for Interacting Particle Systems, Preprint, 1998.
Georgii, H.O.: Canonical Gibbs Measures, Lecture Notes in Mathematics 760, Springer-Verlag, 1979.
Kallenberg, O.: Random Measures, Akademie-Verlag, Berlin, fourth edition, 1986.
Matthes, K., Mecke, J. and Warmuth, W.: 'Bemerkungen zu einer Arbeit von Nguyen Xuan Xanh und Hans Zessin', Math. Nachr. 88(1979), 117-127.
Mecke, J.: 'Stationäre zufällige Masse auf lokalkompakten Abelschen Gruppen', Z. Wahrscheinlichkeitstheorie Verw. Geb. 9(1967), 36-58.
Nguyen, X.X. and Zessin, H.: 'Martin-Dynkin boundary of mixed Poisson processes', Z. Wahrscheinlichkeitstheorie Verw. Geb. 37(1977), 191-200.
Nguyen, X.X. and Zessin, H.: 'Integral and differential characterization of the Gibbs process', Math. Nachr. 88(1979), 105-115.
Picard, J.: 'Formules de dualité sur l'espace de Poisson', Ann. Inst. H. Poincaré, Probab. Statist. 32(4) (1996), 509-548.
Picard, J.: 'On the existence of smooth densities for jump processes', Probab. Theory Related Fields 105(1996), 481-511.
Preston, C.J.: Random Fields, Lecture Notes in Mathematics 534, Springer-Verlag, 1976.
Privault, N.: 'Equivalence of gradients on configuration spaces', Random Operators and Stochastic Equations 7(3) (1999), 241-262.
Privault, N.: 'A pointwise equivalence of gradients on configuration spaces', C.R. Acad. Sci. Paris Sér. I Math. 327(1998), 677-682.
Roelly, S. and Zessin, H.: 'Une caractérisation des diffusions par le calcul des variations stochastiques', C.R. Acad. Sci. Paris Sér. I Math. 313(5) (1991), 309-312.
Roelly, S. and Zessin, H.: 'Une caractérisation des mesures de Gibbs sur C(0, 1)Zd par le calcul des variations stochastiques', Ann. Inst. Henri Poincaré, Probab. Statist. 29(3) (1993), 327-338.
Roelly, S. and Zessin, H.: 'Une caractérisation de champs gibbsiens sur un espace de trajectoires', C.R. Acad. Sci. Paris Sér. I Math. 321(1995), 1377-1382.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Privault, N. A Characterization of Grand Canonical Gibbs Measures by Duality. Potential Analysis 15, 23–38 (2001). https://doi.org/10.1023/A:1011290906171
Issue Date:
DOI: https://doi.org/10.1023/A:1011290906171