{"paper":{"title":"Statistical exponential formulas for homogeneous diffusion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Matthew Rudd","submitted_at":"2014-03-07T19:42:18Z","abstract_excerpt":"Let $\\Delta^{1}_{p}$ denote the $1$-homogeneous $p$-Laplacian, for $1 \\leq p \\leq \\infty$. This paper proves that the unique bounded, continuous viscosity solution $u$ of the Cauchy problem \\[ \\left\\{ \\begin{array}{c} u_{t} \\ - \\ ( \\frac{p}{ \\, N + p - 2 \\, } ) \\, \\Delta^{1}_{p} u ~ = ~ 0 \\quad \\mbox{for} \\quad x \\in \\mathbb{R}^{N}, \\quad t > 0 \\\\ \\\\ u(\\cdot,0) ~ = ~ u_{0} \\in BUC( \\mathbb{R}^{N} ) \\end{array} \\right. \\] is given by the exponential formula \\[ u(t) ~ := ~ \\lim_{n \\to \\infty}{ \\left( M^{t/n}_{p} \\right)^{n} u_{0} } \\, \\] where the statistical operator $M^{h}_{p} \\colon BUC( \\mat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.1853","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"}