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• W3103247990 abstract "We consider Gibbs distributions on permutations of a locally finite infinite set $Xsubsetmathbb{R}$, where a permutation $sigma $ of $X$ is assigned (formal) energy $sum_{xin X}V(sigma (x)-x)$. This is motivated by Feynman’s path representation of the quantum Bose gas; the choice $X:=mathbb{Z}$ and $V(x):=alpha x^{2}$ 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." @default.
• W3103247990 created "2020-11-23" @default.
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• W3103247990 date "2015-04-01" @default.
• W3103247990 modified "2023-09-27" @default.
• W3103247990 title "Gibbs measures on permutations over one-dimensional discrete point sets" @default.
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• W3103247990 doi "https://doi.org/10.1214/14-aap1013" @default.
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