Gibbs states over the cone of discrete measures

Hagedorn D, Kondratiev Y, Pasurek T, Röckner M (2013)
Journal Of Functional Analysis 264(11): 2550-2583.

Zeitschriftenaufsatz | Veröffentlicht| Englisch
 
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Abstract / Bemerkung
We construct Gibbs perturbations of the Gamma process on R-d, which may be used in applications to model systems of densely distributed particles. First we propose a definition of Gibbs measures over the cone of discrete Radon measures on R-d and then analyze conditions for their existence. Our approach works also for general Levy processes instead of Gamma measures. To this end, we need only the assumption that the first two moments of the involved Levy intensity measures are finite. Also uniform moment estimates for the Gibbs distributions are obtained, which are essential for the construction of related diffusions. Moreover, we prove a Mecke type characterization for the Gamma measures on the cone and an FKG inequality for them. (C) 2013 Elsevier Inc. All rights reserved.
Stichworte
configuration spaces; Interacting particle systems; Mecke identity; states; Gibbs; Discrete Radon measures; Poisson point process; Gamma process; DLR equation; Marked; FKG inequality
Erscheinungsjahr
2013
Zeitschriftentitel
Journal Of Functional Analysis
Band
264
Ausgabe
11
Seite(n)
2550-2583
ISSN
0022-1236
Page URI
https://pub.uni-bielefeld.de/record/2584527

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Hagedorn D, Kondratiev Y, Pasurek T, Röckner M. Gibbs states over the cone of discrete measures. Journal Of Functional Analysis. 2013;264(11):2550-2583.
Hagedorn, D., Kondratiev, Y., Pasurek, T., & Röckner, M. (2013). Gibbs states over the cone of discrete measures. Journal Of Functional Analysis, 264(11), 2550-2583. doi:10.1016/j.jfa.2013.03.002
Hagedorn, D., Kondratiev, Y., Pasurek, T., and Röckner, M. (2013). Gibbs states over the cone of discrete measures. Journal Of Functional Analysis 264, 2550-2583.
Hagedorn, D., et al., 2013. Gibbs states over the cone of discrete measures. Journal Of Functional Analysis, 264(11), p 2550-2583.
D. Hagedorn, et al., “Gibbs states over the cone of discrete measures”, Journal Of Functional Analysis, vol. 264, 2013, pp. 2550-2583.
Hagedorn, D., Kondratiev, Y., Pasurek, T., Röckner, M.: Gibbs states over the cone of discrete measures. Journal Of Functional Analysis. 264, 2550-2583 (2013).
Hagedorn, Dennis, Kondratiev, Yuri, Pasurek, Tatiana, and Röckner, Michael. “Gibbs states over the cone of discrete measures”. Journal Of Functional Analysis 264.11 (2013): 2550-2583.