{"ID":23638587,"CreatedAt":"2026-09-18T07:21:59.209084423Z","UpdatedAt":"2026-09-18T07:21:59.209084423Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2609.20657","arxiv_id":"2609.20657","title":"The skeleton-blocks decomposition of Bienaymé trees, and applications to their local convergence","abstract":"We study multi-type critical Bienaymé trees through the lens of the skeleton-blocks structure, seeing them as a monotype skeleton on which we have added multi-type blocks. This decomposition enjoys a remarkably elegant compatibility with the concept of local convergence, allowing us to find simple proofs of traditional local limit theorems.","short_abstract":"We study multi-type critical Bienaymé trees through the lens of the skeleton-blocks structure, seeing them as a monotype skeleton on which we have added multi-type blocks. This decomposition enjoys a remarkably elegant compatibility with the concept of local convergence, allowing us to find simple proofs of traditional...","url_abs":"https://arxiv.org/abs/2609.20657","url_pdf":"https://arxiv.org/pdf/2609.20657v1","authors":"[\"Marc Bernard\",\"Robin Stephenson\"]","published":"2026-09-17T16:37:48Z","proceeding":"math.PR","tasks":"[\"math.PR\"]","methods":"[\"Generative Adversarial Network\"]","has_code":false}