{"paper":{"title":"Meteor process on ${\\mathbb Z}^d$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Krzysztof Burdzy","submitted_at":"2013-12-24T18:12:13Z","abstract_excerpt":"The meteor process is a model for mass redistribution on a graph. The case of finite graphs was analyzed in \\cite{BBPS}. This paper is devoted to the meteor process on ${\\mathbb Z}^d$. The process is constructed and a stationary distribution is found. Convergence to this stationary distribution is proved for a large family of initial distributions. The first two moments of the mass distribution at a vertex are computed for the stationary distribution. For the one-dimensional lattice ${\\mathbb Z}$, the net flow of mass between adjacent vertices is shown to have bounded variance as time goes to "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.6865","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"}