{"paper":{"title":"Binary jumps in continuum. II. Non-equilibrium process and a Vlasov-type scaling limit","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Dmitri Finkelshtein, Eugene Lytvynov, Oleksandr Kutoviy, Yuri Kondratiev","submitted_at":"2011-07-20T15:36:07Z","abstract_excerpt":"Let $\\Gamma$ denote the space of all locally finite subsets (configurations) in $\\mathbb R^d$. A stochastic dynamics of binary jumps in continuum is a Markov process on $\\Gamma$ in which pairs of particles simultaneously hop over $\\mathbb R^d$. We discuss a non-equilibrium dynamics of binary jumps. We prove the existence of an evolution of correlation functions on a finite time interval. We also show that a Vlasov-type mesoscopic scaling for such a dynamics leads to a generalized Boltzmann non-linear equation for the particle density."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.4005","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"}