Gibbs measures on permutations over one-dimensional discrete point sets

T. Richthammer, M. Biskup, Communications in Mathematical Physics 25 (2015) 898–929.

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Journal Article | Published | English
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Abstract
We consider Gibbs distributions on permutations of a locally finite infinite set X⊂R, where a permutation σ of X is assigned (formal) energy ∑x∈XV(σ(x)−x). This is motivated by Feynman’s path representation of the quantum Bose gas; the choice X:=Z and V(x):=αx2 is of principal interest. Under suitable regularity conditions on the set X and the potential V, we establish existence and a full classification of the infinite-volume Gibbs measures for this problem, including a result on the number of infinite cycles of typical permutations. Unlike earlier results, our conclusions are not limited to small densities and/or high temperatures.
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Communications in Mathematical Physics
Volume
25
Issue
2
Page
898-929
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Richthammer T, Biskup M. Gibbs measures on permutations over one-dimensional discrete point sets. Communications in Mathematical Physics. 2015;25(2):898-929. doi:https://doi.org/10.48550/arXiv.1310.0248
Richthammer, T., & Biskup, M. (2015). Gibbs measures on permutations over one-dimensional discrete point sets. Communications in Mathematical Physics, 25(2), 898–929. https://doi.org/10.48550/arXiv.1310.0248
@article{Richthammer_Biskup_2015, title={Gibbs measures on permutations over one-dimensional discrete point sets}, volume={25}, DOI={https://doi.org/10.48550/arXiv.1310.0248}, number={2}, journal={Communications in Mathematical Physics}, publisher={Springer Science+Business Media}, author={Richthammer, Thomas and Biskup, Marek}, year={2015}, pages={898–929} }
Richthammer, Thomas, and Marek Biskup. “Gibbs Measures on Permutations over One-Dimensional Discrete Point Sets.” Communications in Mathematical Physics 25, no. 2 (2015): 898–929. https://doi.org/10.48550/arXiv.1310.0248.
T. Richthammer and M. Biskup, “Gibbs measures on permutations over one-dimensional discrete point sets,” Communications in Mathematical Physics, vol. 25, no. 2, pp. 898–929, 2015, doi: https://doi.org/10.48550/arXiv.1310.0248.
Richthammer, Thomas, and Marek Biskup. “Gibbs Measures on Permutations over One-Dimensional Discrete Point Sets.” Communications in Mathematical Physics, vol. 25, no. 2, Springer Science+Business Media, 2015, pp. 898–929, doi:https://doi.org/10.48550/arXiv.1310.0248.

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