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Probability Theory and Related Fields

, Volume 149, Issue 1–2, pp 191–222 | Cite as

Spatial random permutations with small cycle weights

  • Volker Betz
  • Daniel Ueltschi
Article

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.

Keywords

Random permutations Cycle weights Spatial permutations Infinite cycles 

Mathematics Subject Classification (2000)

60K35 82B20 82B26 82B41 

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Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of WarwickCoventryEngland

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