{"paper":{"title":"Feller property of the multiplicative coalescent with linear deletion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Balazs Rath","submitted_at":"2016-09-30T20:13:17Z","abstract_excerpt":"We modify the definition of Aldous' multiplicative coalescent process and introduce the multiplicative coalescent with linear deletion (MCLD). A state of this process is a square-summable decreasing sequence of cluster sizes. Pairs of clusters merge with a rate equal to the product of their sizes and clusters are deleted with a rate linearly proportional to their size. We prove that the MCLD is a Feller process. This result is a key ingredient in the description of scaling limits of the evolution of component sizes of the mean field frozen percolation model and the so-called rigid representati"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.00021","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"}