{"paper":{"title":"Dependence and phase changes in random $m$-ary search trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Hsien-Kuei Hwang, Hua-Huai Chern, Michael Fuchs, Ralph Neininger","submitted_at":"2015-01-21T11:32:49Z","abstract_excerpt":"We study the joint asymptotic behavior of the space requirement and the total path length (either summing over all root-key distances or over all root-node distances) in random $m$-ary search trees. The covariance turns out to exhibit a change of asymptotic behavior: it is essentially linear when $3\\le m\\le 13$ but becomes of higher order when $m\\ge14$. Surprisingly, the corresponding asymptotic correlation coefficient tends to zero when $3\\le m\\le 26$ but is periodically oscillating for larger $m$. Such a less anticipated phenomenon is not exceptional and we extend the results in two directio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.05135","kind":"arxiv","version":3},"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"}