Communications in Mathematical Physics

, Volume 285, Issue 2, pp 469–501 | Cite as

Spatial Random Permutations and Infinite Cycles

  • Volker Betz
  • Daniel Ueltschi


We consider systems of spatial random permutations, where permutations are weighed according to the point locations. Infinite cycles are present at high densities. The critical density is given by an exact expression. We discuss the relation between the model of spatial permutations and the ideal and interacting quantum Bose gas.


Point Process Critical Density Occupation Number Fourier Mode Spatial Permutation 
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© Springer-Verlag 2008

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of WarwickCoventryEngland

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