{"paper":{"title":"Conditions for permanental processes to be unbounded","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jay Rosen, Michael B. Marcus","submitted_at":"2015-11-16T21:04:28Z","abstract_excerpt":"An $\\al$-permanental process $\\{X_{ t},t\\in T \\}$ is a stochastic process determined by a kernel $K=\\{K(s,t),s,t\\in T \\}$, with the property that for all $t_{1},\\ldots,t_{n}\\in T $, $ |I+K( t_{1},\\ldots,t_{n}) S|^{- \\al} $ is the Laplace transform of $(X_{t_{1}},\\ldots,X_{t_{n}})$, where $ K( t_{1},\\ldots,t_{n})$ denotes the matrix $\\{K(t_{i}, t_{j})\\}_{i,j=1}^{n}$ and $S$ is the diagonal matrix with entries $s_{1},\\ldots,s_{n} $. $ (X_{t_{1}},\\ldots,X_{t_{n}})$ is called a permanental vector.\n  Under the condition that $K$ is the potential density of a transient Markov process,\n  $(X_{t_{1}},"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.05172","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"}