{"paper":{"title":"Spreading maps (polymorphisms), symmetries of Poisson processes and matching summation","license":"","headline":"","cross_cats":["math.DS","math.FA","math.MP","math.PR","math.RT"],"primary_cat":"math-ph","authors_text":"Yurii A. Neretin","submitted_at":"2001-12-20T13:07:49Z","abstract_excerpt":"The matrix of a permutation is a partial case of Markov transition matrices. In the same way, a measure preserving bijection of a space A with finite measure is a partial case of Markov transition operators. A Markov transition operator also can be considered as a map (polymorphism) A to A, which spreads points of A into measures on A.\n  In this paper, we discuss R-polymorphisms and $\\vee$-polymorphisms, who are analogues of the Markov transition operators for the groups of bijections A to A leaving the measure quasiinvariant; two types of the polymorphisms correspond to the cases, when A has "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0112046","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"}