{"paper":{"title":"Random jumps and coalescence in the continuum: evolution of states of an infinite system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Krzysztof Pilorz, Yuri Kozitsky","submitted_at":"2018-07-19T09:25:01Z","abstract_excerpt":"The dynamics of an infinite continuum system of randomly jumping and coalescing point particles is studied. The states of the system are probability measures on the corresponding configuration space $\\Gamma$ the evolution of which is constructed in the following way. The evolution of observables $F_0\\to F_t$ is obtained from a Kolmogorov-type evolution equation. Then the evolution of states $\\mu_0\\to \\mu_t$ is defined by the relation $\\mu_0(F_t) =\\mu_t(F_0)$ for $F_0$ belonging to a measure-defining class of functions. The main result of the paper is the proof of the existence of the evolution"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.07310","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"}