{"paper":{"title":"Free Jump Dynamics in Continuum","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.DS","authors_text":"Joanna Baranska, Yuri Kozitsky","submitted_at":"2014-08-27T08:41:05Z","abstract_excerpt":"The evolution is described of an infinite system of hopping point particles in $\\mathbb{R}^d$. The states of the system are probability measures on the space of configurations of particles. Under the condition that the initial state $\\mu_0$ has correlation functions of all orders which are: (a) $k_{\\mu_0}^{(n)} \\in L^\\infty ((\\mathbb{R}^d)^n)$ (essentially bounded); (b) $\\|k_{\\mu_0}^{(n)}\\|_{ L^\\infty ((\\mathbb{R}^d)^n)} \\leq C^n$, $n\\in \\mathbb{N}$ (sub-Poissonian), the evolution $\\mu_0 \\mapsto \\mu_t$, $t>0$, is obtained as a continuously differentiable map $k_{\\mu_0} \\mapsto k_t$, $k_t =(k_t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.6346","kind":"arxiv","version":1},"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"}