{"paper":{"title":"Permanental fields, loop soups and continuous additive functionals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jay Rosen, Michael B. Marcus, Yves Le Jan","submitted_at":"2012-09-09T14:50:04Z","abstract_excerpt":"A permanental field, $\\psi=\\{\\psi(\\nu),\\nu\\in {\\mathcal{V}}\\}$, is a particular stochastic process indexed by a space of measures on a set $S$. It is determined by a kernel $u(x,y)$, $x,y\\in S$, that need not be symmetric and is allowed to be infinite on the diagonal. We show that these fields exist when $u(x,y)$ is a potential density of a transient Markov process $X$ in $S$. A permanental field $\\psi$ can be realized as the limit of a renormalized sum of continuous additive functionals determined by a loop soup of $X$, which we carefully construct. A Dynkin-type isomorphism theorem is obtain"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.1804","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"}