{"paper":{"title":"Ergodic unitarily invariant measures on the space of infinite Hermitian matrices","license":"","headline":"","cross_cats":["math.CA","math.PR"],"primary_cat":"math.RT","authors_text":"Anatoli Vershik, Grigori Olshanski","submitted_at":"1996-01-07T00:00:00Z","abstract_excerpt":"Let $H$ be the space of all Hermitian matrices of infinite order and $U(\\infty)$ be the inductive limit of the chain $U(1)\\subset U(2)\\subset...$ of  compact unitary groups. The group $U(\\infty)$ operates on the space $H$ by conjugations, and our aim is to classify the ergodic $U(\\infty)$-invariant probability measures on $H$ by making use of a general asymptotic approach proposed in Vershik's note \\cite{V}. The problem is reduced to studying the limit behavior of orbital integrals of the form\n  $$\\int_{B\\in\\Omega_n}e^{i\\op{tr}(AB)}M_n(dB),$$\n  where $A$ is a fixed $\\infty\\times\\infty$ Hermiti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9601215","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"}