{"paper":{"title":"Coagulation processes with Gibbsian time evolution","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Alexander Kryvoshaev, Boris Granovsky","submitted_at":"2010-08-05T17:26:45Z","abstract_excerpt":"We prove that time dynamics of a stochastic process of pure coagulation is given by a time dependent Gibbs distribution if and only if rates of single coagulations have the form $\\psi(i,j)=if(j)+jf(i)$, where $f$ is an arbitrary nonnegative function on the set of integers $\\ge 1$. We also obtained a recurrence relation for weights of these Gibbs distributions, that allowed explicit solutions in three particular cases of the function $f$. For the three corresponding models, we study the probability of coagulation into one giant cluster, at time $t>0.$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.1027","kind":"arxiv","version":2},"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"}