{"paper":{"title":"Summability of joint cumulants of nonindependent lattice fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Alessia Nota, Jani Lukkarinen, Matteo Marcozzi","submitted_at":"2016-01-29T15:45:59Z","abstract_excerpt":"We consider two nonindependent random fields $\\psi$ and $\\phi$ defined on a countable set $Z$. For instance, $Z={\\mathbb Z}^d$ or $Z={\\mathbb Z}^d\\times I$, where $I$ denotes a finite set of possible \"internal degrees of freedom\" such as spin. We prove that, if the cumulants of both $\\psi$ and $\\phi$ are $\\ell_1$-clustering up to order $2 n$, then all joint cumulants between $\\psi$ and $\\phi$ are $\\ell_2$-summable up to order $n$, in the precise sense described in the text. We also provide explicit estimates in terms of the related $\\ell_1$-clustering norms, and derive a weighted $\\ell_2$-summ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.08163","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"}