{"paper":{"title":"The critical one-dimensional multi-particle DLA","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Allan Sly, Danny Nam, Dor Elboim","submitted_at":"2020-09-06T15:56:33Z","abstract_excerpt":"We study one-dimensional multi-particle Diffusion Limited Aggregation (MDLA) at its critical density $\\lambda=1$. Previous works have verified that the size of the aggregate $X_t$ at time $t$ is $t^{1/2}$ in the subcritical regime and linear in the supercritical regime. This paper establishes the conjecture that the growth rate at criticiality is $t^{2/3}$. Moreover, we derive the scaling limit proving that\n  $$\\big\\{ t^{-2/3}X_{st} \\big\\}_{s\\geq 0} \\overset{d}{\\rightarrow} \\Big\\{ \\int_0^s Z_u du \\Big\\}_{s\\geq 0}, $$ where the speed process $\\{Z_t\\}$ is a $(-\\frac{1}{3})$-self-similar diffusio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2009.02761","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/2009.02761/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"}