{"paper":{"title":"Diffusion Limited Aggregation on a Cylinder","license":"","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Ariel Yadin, Itai Benjamini","submitted_at":"2007-01-07T08:32:18Z","abstract_excerpt":"We consider the DLA process on a cylinder G x N. It is shown that this process \"grows arms\", provided that the base graph G has small enough mixing time. Specifically, if the mixing time of G is at most (log|G|)^(2-\\eps), the time it takes the cluster to reach the m-th layer of the cylinder is at most of order m |G|/loglog|G|. In particular we get examples of infinite Cayley graphs of degree 5, for which the DLA cluster on these graphs has arbitrarily small density.\n  In addition, we provide an upper bound on the rate at which the \"arms\" grow. This bound is valid for a large class of base grap"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0701201","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/0701201/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}