{"paper":{"title":"A Schur transform for spatial stochastic processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"James Mathews","submitted_at":"2018-11-15T08:07:51Z","abstract_excerpt":"The variance, higher order moments, covariance, and joint moments or cumulants are shown to be special cases of a certain tensor in $V^{\\otimes n}$ defined in terms of a collection $X_1,...,X_n$ of $V$-valued random variables, for an appropriate finite-dimensional real vector space $V$. A statistical transform is proposed from such collections--finite spatial stochastic processes--to numerical tuples using the Schur-Weyl decomposition of $V^{\\otimes n}$. It is analogous to the Fourier transform, replacing the periodicity group $\\mathbb{Z}$, $\\mathbb{R}$, or $U(1)$ with the permutation group $S"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.06221","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"}