# Shift in Critical Temperature for Random Spatial Permutations with Cycle Weights

@article{Kerl2010ShiftIC, title={Shift in Critical Temperature for Random Spatial Permutations with Cycle Weights}, author={John Kerl}, journal={Journal of Statistical Physics}, year={2010}, volume={140}, pages={56-75} }

We examine a phase transition in a model of random spatial permutations which originates in a study of the interacting Bose gas. Permutations are weighted according to point positions; the low-temperature onset of the appearance of arbitrarily long cycles is connected to the phase transition of Bose-Einstein condensates. In our simplified model, point positions are held fixed on the fully occupied cubic lattice and interactions are expressed as Ewens-type weights on cycle lengths of…

## 4 Citations

Lattice Permutations and Poisson-Dirichlet Distribution of Cycle Lengths

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We study random spatial permutations on ℤ3 where each jump x↦π(x) is penalized by a factor $\mathrm{e}^{-T\| x-\pi (x)\|^{2}}$. The system is known to exhibit a phase transition for low enough T…

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Spatial random permutations were originally studied due to their connections to Bose–Einstein condensation, but they possess many interesting properties of their own. For random permutations of a…

SPATIAL RANDOM PERMUTATIONS AND POISSON-DIRICHLET LAW OF CYCLE LENGTHS

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- 2011

We study spatial permutations with cycle weights that are bounded or slowly diverging. We show that a phase transition occurs at an explicit critical density. The long cycles are macroscopic and…

A Complete Bibliography of the Journal of Statistical Physics: 2000{2009

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