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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 12). pp. 191222. ISSN 01788051
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Official URL: http://dx.doi.org/10.1007/s0044000902480
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  

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:  01788051  
Official Date:  February 2011  
Dates: 


Volume:  Volume 149  
Number:  Numbers 12  
Page Range:  pp. 191222  
Identification Number:  10.1007/s0044000902480  
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), DMS0601075 (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 
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