{"paper":{"title":"Convergence of the empirical spectral distribution of Gaussian matrix-valued processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Arturo Jaramillo, Jos\\'e Luis P\\'erez, Juan Carlos Pardo","submitted_at":"2018-01-07T01:52:14Z","abstract_excerpt":"For a given normalized Gaussian symmetric matrix-valued process $Y^{(n)}$, we consider the process of its eigenvalues $\\{(\\lambda_{1}^{(n)}(t),\\dots, \\lambda_{n}^{(n)}(t)); t\\ge 0\\}$ as well as its corresponding process of empirical spectral measures $\\mu^{(n)}=(\\mu_{t}^{(n)}; t\\geq0)$. Under some mild conditions on the covariance function associated to $Y^{(n)}$, we prove that the process $\\mu^{(n)}$ converges in probability to a deterministic limit $\\mu$, in the topology of uniform convergence over compact sets. We show that the process $\\mu$ is characterized by its Cauchy transform, which i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.02111","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"}