Skip to main content

Advertisement

SpringerLink
Log in
Menu
Find a journal Publish with us
Search
Cart
  1. Home
  2. Probability Theory and Related Fields
  3. Article
Random permutations of countable sets
Download PDF
Download PDF
  • Published: March 1991

Random permutations of countable sets

  • Karl-Heinz Fichtner1 

Probability Theory and Related Fields volume 89, pages 35–60 (1991)Cite this article

  • 91 Accesses

  • 9 Citations

  • Metrics details

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.

Download to read the full article text

Working on a manuscript?

Avoid the common mistakes

References

  1. Fichtner, K.-H., Freudenberg, W.: Point processes and normal states of boson systems. (preprint NTZ d. K.-M.-Universität Leipzig)

  2. Fichtner, K.-H., Freudenberg, W.: Point processes and states of infinite boson systems. (preprint NTZ d. K.-M.-Universität Leipzig)

  3. Matthes, K., Kerstan, J., Mecke, J.: Infinitely divisible point processes. New York: J. Wiley 1978

    Google Scholar 

  4. Kerstan, J., Wakolbinger, A.: Ergodic decomposition of probability laws. Z. Wahrscheinlichkeitstheor. Verw. Geb.56, 399–414 (1981)

    Google Scholar 

  5. Fichtner, K.-H.: On the position distribution of the ideal Bose gas. Math. Nachr. (to appear)

Download references

Author information

Authors and Affiliations

  1. Mathematische Fakultät, Friedrich-Schiller-Universität Jena, Schillerstrasse, O-6900, Jena, Germany

    Karl-Heinz Fichtner

Authors
  1. Karl-Heinz Fichtner
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints 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

Download citation

  • Received: 16 January 1990

  • Revised: 10 December 1990

  • Issue Date: March 1991

  • DOI: https://doi.org/10.1007/BF01225824

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

Keywords

  • Stochastic Process
  • Probability Theory
  • Mathematical Biology
  • Random Point
  • Random Permutation
Download PDF

Working on a manuscript?

Avoid the common mistakes

Advertisement

Search

Navigation

  • Find a journal
  • Publish with us

Discover content

  • Journals A-Z
  • Books A-Z

Publish with us

  • Publish your research
  • Open access publishing

Products and services

  • Our products
  • Librarians
  • Societies
  • Partners and advertisers

Our imprints

  • Springer
  • Nature Portfolio
  • BMC
  • Palgrave Macmillan
  • Apress
  • Your US state privacy rights
  • Accessibility statement
  • Terms and conditions
  • Privacy policy
  • Help and support

167.114.118.210

Not affiliated

Springer Nature

© 2023 Springer Nature