Summary
The main objective of this paper is a study of random decompositions of random point configurations onR d into finite clusters. This is achieved by constructing for each configurationZ a random permutation ofZ with finite cycles; these cycles then form the cluster decomposition ofZ. It is argued that a good candidate for a random permutation ofZ is a Gibbs measure for a certain specification, and conditions are given for the existence and uniqueness of such a Gibbs measure. These conditions are then verified for certain random configurationsZ.
Article PDF
Similar content being viewed by others
References
Fichtner, K.-H., Freudenberg, W.: Point processes and normal states of boson systems. (preprint NTZ d. K.-M.-Universität Leipzig)
Fichtner, K.-H., Freudenberg, W.: Point processes and states of infinite boson systems. (preprint NTZ d. K.-M.-Universität Leipzig)
Matthes, K., Kerstan, J., Mecke, J.: Infinitely divisible point processes. New York: J. Wiley 1978
Kerstan, J., Wakolbinger, A.: Ergodic decomposition of probability laws. Z. Wahrscheinlichkeitstheor. Verw. Geb.56, 399–414 (1981)
Fichtner, K.-H.: On the position distribution of the ideal Bose gas. Math. Nachr. (to appear)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Fichtner, KH. Random permutations of countable sets. Probab. Th. Rel. Fields 89, 35–60 (1991). https://doi.org/10.1007/BF01225824
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01225824