{"paper":{"title":"Kemeny's constant for one-dimensional diffusions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ross G. Pinsky","submitted_at":"2019-03-28T14:29:04Z","abstract_excerpt":"Let $X(\\cdot)$ be a non-degenerate, positive recurrent one-dimensional diffusion process on $\\mathbb{R}$ with invariant probability density $\\mu(x)$, and let $\\tau_y=\\inf\\{t\\ge0: X(t)=y\\}$ denote the first hitting time of $y$. Let $\\mathcal{X}$ be a random variable independent of the diffusion process $X(\\cdot)$ and distributed according to the process's invariant probability measure $\\mu(x)dx$. Denote by $\\mathcal{E}^\\mu$ the expectation with respect to $\\mathcal{X}$. Consider the expression $$ \\mathcal{E}^\\mu E_x\\tau_\\mathcal{X}=\\int_{-\\infty}^\\infty (E_x\\tau_y)\\mu(y)dy, \\ x\\in\\mathbb{R}. $$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.12005","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"}