{"paper":{"title":"A characterization of the normal distribution using stationary max-stable processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Sebastian Engelke, Zakhar Kabluchko","submitted_at":"2015-08-18T10:07:54Z","abstract_excerpt":"Consider the max-stable process $\\eta(t) = \\max_{i\\in\\mathbb N} U_i \\rm{e}^{\\langle X_i, t\\rangle - \\kappa(t)}$, $t\\in\\mathbb{R}^d$, where $\\{U_i, i\\in\\mathbb{N}\\}$ are points of the Poisson process with intensity $u^{-2}\\rm{d} u$ on $(0,\\infty)$, $X_i$, $i\\in\\mathbb{N}$, are independent copies of a random $d$-variate vector $X$ (that are independent of the Poisson process), and $\\kappa: \\mathbb{R}^d \\to \\mathbb{R}$ is a function. We show that the process $\\eta$ is stationary if and only if $X$ has multivariate normal distribution and $\\kappa(t)-\\kappa(0)$ is the cumulant generating function o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.04266","kind":"arxiv","version":2},"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"}