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### Spatial random permutations with small cycle weights

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Betz, Volker and Ueltschi, Daniel.
(2011)
*Spatial random permutations with small cycle weights.*
Probability Theory and Related Fields, Volume 149
(Numbers 1-2).
pp. 191-222.
ISSN 0178-8051

**Full text not available from this repository.**

Official URL: http://dx.doi.org/10.1007/s00440-009-0248-0

## 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.

Item Type: | Journal Article |
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Subjects: | Q Science > QA Mathematics |

Divisions: | Faculty of Science > Mathematics |

Library of Congress Subject Headings (LCSH): | Permutations |

Journal or Publication Title: | Probability Theory and Related Fields |

Publisher: | Springer |

ISSN: | 0178-8051 |

Official Date: | February 2011 |

Volume: | Volume 149 |

Number: | Numbers 1-2 |

Page Range: | pp. 191-222 |

Identification Number: | 10.1007/s00440-009-0248-0 |

Status: | Peer Reviewed |

Publication Status: | Published |

Access rights to Published version: | Restricted or Subscription Access |

Funder: | Engineering and Physical Sciences Research Council (EPSRC), National Science Foundation (U.S.) (NSF) |

Grant number: | EP/D07181X/1 (EPSRC), DMS-0601075 (NSF) |

References: | 1. Baik, J., Deift, P., Johannson, K.: On the distribution of the length of the longest increasing subsequence |

URI: | http://wrap.warwick.ac.uk/id/eprint/41514 |

Data sourced from Thomson Reuters' Web of Knowledge

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