{"paper":{"title":"What is a $p$-adic Dyson Brownian motion?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.NT"],"primary_cat":"math.PR","authors_text":"Roger Van Peski","submitted_at":"2023-09-06T09:45:33Z","abstract_excerpt":"We consider the singular numbers of a certain explicit continuous-time Markov jump process on $\\mathrm{GL}_N(\\mathbb{Q}_p)$, which we argue gives the closest $p$-adic analogue of multiplicative Dyson Brownian motion. We do so by explicitly classifying the possible dynamics of singular numbers of processes on $\\mathrm{GL}_N(\\mathbb{Q}_p)$ satisfying natural properties possessed by Brownian motion on $\\mathrm{GL}_N(\\mathbb{C})$. Computing the evolution of singular numbers explicitly, we find that the $N$-tuple of singular numbers in decreasing order evolves as a Poisson jump process on $\\mathbb{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2309.02865","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/2309.02865/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"}