{"paper":{"title":"Limit laws for discrete excursions and meanders and linear functional equations with a catalytic variable","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Uwe Schwerdtfeger","submitted_at":"2011-05-26T00:09:57Z","abstract_excerpt":"We study limit distributions for random variables defined in terms of coefficients of a power series which is determined by a certain linear functional equation. Our technique combines the method of moments with the kernel method of algebraic combinatorics. As limiting distributions the area distributions of the Brownian excursion and meander occur. As combinatorial applications we compute the area laws for discrete excursions and meanders with an arbitrary finite set of steps and the area distribution of column convex polyominoes. As a by-product of our approach we find the joint distribution"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.5175","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"}