{"paper":{"title":"Time scales in large systems of Brownian particles with stochastic synchronization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Anatoly Manita","submitted_at":"2010-12-14T19:24:07Z","abstract_excerpt":"We consider a system $x(t)=(x_{1}(t),...,x_{N}(t))$ consisting of $N$ Brownian particles with synchronizing interaction between them occurring at random time moments $\\{\\tau_{n}\\}_{n=1}^{\\infty}$. Under assumption that the free Brownian motions and the sequence $\\{\\tau_{n}\\}_{n=1}^{\\infty}$ are independent we study asymptotic properties of the system when both the dimension~$N$ and the time~$t$ go to infinity. We find three time scales $t=t(N)$ of qualitatively different behavior of the system."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.3140","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"}