{"paper":{"title":"Local Large Deviations: McMillian Theorem for multitype Galton-Watson Processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Kwabena Doku-Amponsah","submitted_at":"2017-05-28T17:39:19Z","abstract_excerpt":"In this article we prove a local large deviation principle (LLDP) for the critical multitype Galton-Watson process from spectral potential point. We define the so-called a spectral potential $U_{\\skrik}(\\,\\cdot,\\,\\pi)$ for the Galton-Watson process, where $\\pi$ is the normalized eigen vector corresponding to the leading \\emph{Perron-Frobenius eigen value } $\\1$ of the transition matrix $\\skria(\\cdot,\\,\\cdot)$ defined from ${\\skrik},$ the transition kernel. We show that the Kullback action or the deviation function, $J(\\pi,\\rho),$ with respect to an empirical offspring measure, $\\rho,$ is the L"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.09967","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"}