{"paper":{"title":"Heat content asymptotics of some random Koch type snowflakes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Philippe H. A. Charmoy","submitted_at":"2014-03-07T17:14:19Z","abstract_excerpt":"We consider the short time asymptotics of the heat content $E$ of a domain $D$ of $\\mathbb{R}^d$. The novelty of this paper is that we consider the situation where $D$ is a domain whose boundary $\\partial D$ is a random Koch type curve.\n  When $\\partial D$ is spatially homogeneous, we show that we can recover the lower and upper Minkowski dimensions of $\\partial D$ from the short time behaviour of $E(s)$. Furthermore, in some situations where the Minkowski dimension exists, finer geometric fluctuations can be recovered and the heat content is controlled by $s^\\alpha e^{f(\\log(1/s))}$ for small"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.1811","kind":"arxiv","version":1},"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"}