{"paper":{"title":"Limit distributions for Euclidean random permutations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Dor Elboim, Ron Peled","submitted_at":"2017-12-11T15:06:14Z","abstract_excerpt":"We study the length of cycles in the model of spatial random permutations in Euclidean space. In this model, for given length $L$, density $\\rho$, dimension $d$ and jump density $\\varphi$, one samples $\\rho L^d$ particles in a $d$-dimensional torus of side length $L$, and a permutation $\\pi$ of the particles, with probability density proportional to the product of values of $\\varphi$ at the differences between a particle and its image under $\\pi$. The distribution may be further weighted by a factor of $\\theta$ to the number of cycles in $\\pi$. Following Matsubara and Feynman, the emergence of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.03809","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}