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Spatial random permutations with small cycle weights
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  • Published: 13 October 2009

Spatial random permutations with small cycle weights

  • Volker Betz1 &
  • Daniel Ueltschi1 

Probability Theory and Related Fields volume 149, pages 191–222 (2011)Cite this article

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  • 17 Citations

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Abstract

We consider the distribution of cycles in two models of random permutations, that are related to one another. In the first model, cycles receive a weight that depends on their length. The second model deals with permutations of points in the space and there is an additional weight that involves the length of permutation jumps. We prove the occurrence of infinite macroscopic cycles above a certain critical density.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Warwick, Coventry, CV4 7AL, England

    Volker Betz & Daniel Ueltschi

Authors
  1. Volker Betz
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  2. Daniel Ueltschi
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Corresponding author

Correspondence to Daniel Ueltschi.

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Cite this article

Betz, V., Ueltschi, D. Spatial random permutations with small cycle weights. Probab. Theory Relat. Fields 149, 191–222 (2011). https://doi.org/10.1007/s00440-009-0248-0

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  • Received: 02 December 2008

  • Revised: 03 August 2009

  • Published: 13 October 2009

  • Issue Date: February 2011

  • DOI: https://doi.org/10.1007/s00440-009-0248-0

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Keywords

  • Random permutations
  • Cycle weights
  • Spatial permutations
  • Infinite cycles

Mathematics Subject Classification (2000)

  • 60K35
  • 82B20
  • 82B26
  • 82B41
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