{"paper":{"title":"Hua-Pickrell diffusions and differential equations related with pseudo-Jacobi polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.CA","math.MP"],"primary_cat":"math.PR","authors_text":"Martin Auer, Michael Voit","submitted_at":"2026-02-16T13:04:34Z","abstract_excerpt":"Following Assiotis (2020), we study general $\\beta$-Hua-Pickrell diffusions of $N$ particles on $\\mathbb R$ as solutions of the stochastic differential equations (SDEs) $$dX_{j,t}=\\sqrt{2(1+X_{j,t}^2)}\\,dB_{j,t}+\\beta\\left[b-a X_{j,t}+\\sum_{l=1,\\ldots, N; \\> l\\neq j}\\frac{X_{j,t}X_{l,t}+1}{X_{j,t}-X_{l,t}}\\right]dt\\,,\\;\\; (j=1,\\ldots,N)$$ with $\\beta\\ge 1,\\> a,b\\in\\mathbb R$. These processes form a subclass of the Pearson diffusions which are defined as solutions of algebraic SDEs where the moments of the empirical distributions $\\mu_t^N:=\\frac{1}{N}\\sum_{j=1}^N \\delta_{X_{j,t}}$ can be comput"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2602.14719","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2602.14719/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}