{"paper":{"title":"Near log-convexity of measured heat in (discrete) time and consequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"cs.CC","authors_text":"Mert Sa\\u{g}lam","submitted_at":"2018-08-20T23:07:10Z","abstract_excerpt":"Let $u,v \\in \\mathbb{R}^\\Omega_+$ be positive unit vectors and $S\\in\\mathbb{R}^{\\Omega\\times\\Omega}_+$ be a symmetric substochastic matrix. For an integer $t\\ge 0$, let $m_t = \\smash{\\left\\langle v,S^tu\\right\\rangle}$, which we view as the heat measured by $v$ after an initial heat configuration $u$ is let to diffuse for $t$ time steps according to $S$. Since $S$ is entropy improving, one may intuit that $m_t$ should not change too rapidly over time. We give the following formalizations of this intuition.\n  We prove that $m_{t+2} \\ge m_t^{1+2/t}\\!,$ an inequality studied earlier by Blakley and"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.06717","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"}