{"paper":{"title":"The Singular Values of L\\'evy's Area Matrix","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Danilo Jr Dela Cruz, Harald Oberhauser","submitted_at":"2026-06-08T02:09:51Z","abstract_excerpt":"The matrix of L\\'evy's areas of $d$-dimensional Brownian motion is a fundamental object in stochastic analysis. In this article, we study the singular values of this $d \\times d$ skew-symmetric random matrix. First, we derive an explicit formula for the density of the singular values and, en passant, present a new short proof of the characteristic function of L\\'evy's area when $d \\ge 3$. This also allows us to extend the well-known formula for the density of L\\'evy's area to $d \\ge 3$. Next, we use these results to characterise the singular spectrum as a determinantal point process with its k"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.08928","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.08928/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"}