{"page":"898-929","doi":"https://doi.org/10.48550/arXiv.1310.0248","issue":"2","publication_status":"published","date_created":"2022-09-14T04:57:58Z","abstract":[{"text":"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. ","lang":"eng"}],"publication":"Communications in Mathematical Physics","date_updated":"2022-09-14T04:58:02Z","type":"journal_article","language":[{"iso":"eng"}],"citation":{"bibtex":"@article{Richthammer_Biskup_2015, title={Gibbs measures on permutations over one-dimensional discrete point sets}, volume={25}, DOI={<a href=\"https://doi.org/10.48550/arXiv.1310.0248\">https://doi.org/10.48550/arXiv.1310.0248</a>}, number={2}, journal={Communications in Mathematical Physics}, publisher={Springer Science+Business Media}, author={Richthammer, Thomas and Biskup, Marek}, year={2015}, pages={898–929} }","short":"T. Richthammer, M. Biskup, Communications in Mathematical Physics 25 (2015) 898–929.","chicago":"Richthammer, Thomas, and Marek Biskup. “Gibbs Measures on Permutations over One-Dimensional Discrete Point Sets.” <i>Communications in Mathematical Physics</i> 25, no. 2 (2015): 898–929. <a href=\"https://doi.org/10.48550/arXiv.1310.0248\">https://doi.org/10.48550/arXiv.1310.0248</a>.","mla":"Richthammer, Thomas, and Marek Biskup. “Gibbs Measures on Permutations over One-Dimensional Discrete Point Sets.” <i>Communications in Mathematical Physics</i>, vol. 25, no. 2, Springer Science+Business Media, 2015, pp. 898–929, doi:<a href=\"https://doi.org/10.48550/arXiv.1310.0248\">https://doi.org/10.48550/arXiv.1310.0248</a>.","ama":"Richthammer T, Biskup M. Gibbs measures on permutations over one-dimensional discrete point sets. <i>Communications in Mathematical Physics</i>. 2015;25(2):898-929. doi:<a href=\"https://doi.org/10.48550/arXiv.1310.0248\">https://doi.org/10.48550/arXiv.1310.0248</a>","ieee":"T. Richthammer and M. Biskup, “Gibbs measures on permutations over one-dimensional discrete point sets,” <i>Communications in Mathematical Physics</i>, vol. 25, no. 2, pp. 898–929, 2015, doi: <a href=\"https://doi.org/10.48550/arXiv.1310.0248\">https://doi.org/10.48550/arXiv.1310.0248</a>.","apa":"Richthammer, T., &#38; Biskup, M. (2015). Gibbs measures on permutations over one-dimensional discrete point sets. <i>Communications in Mathematical Physics</i>, <i>25</i>(2), 898–929. <a href=\"https://doi.org/10.48550/arXiv.1310.0248\">https://doi.org/10.48550/arXiv.1310.0248</a>"},"user_id":"85821","volume":25,"department":[{"_id":"96"}],"_id":"33359","title":"Gibbs measures on permutations over one-dimensional discrete point sets","author":[{"id":"62054","last_name":"Richthammer","full_name":"Richthammer, Thomas","first_name":"Thomas"},{"first_name":"Marek","full_name":"Biskup, Marek","last_name":"Biskup"}],"publisher":"Springer Science+Business Media","year":"2015","intvolume":"        25","status":"public"}