{"ID":2836149,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.22804","arxiv_id":"2511.22804","title":"Large $n$-limit of matrix control problems and non-commutative controls","abstract":"Building on the free-probability stochastic control framework introduced in arXiv:2502.17329, we connect optimal control problems for $n \\times n$ random matrix ensembles with their infinite-dimensional, free-probability analogues. Under natural convexity hypotheses, we prove that the non-commutative value function captures the large-$n$ limit of the corresponding finite-matrix control problems. As an application, we give a new perspective on the Laplace principle for convex functionals in the theory of large deviations for random matrices.","short_abstract":"Building on the free-probability stochastic control framework introduced in arXiv:2502.17329, we connect optimal control problems for $n \\times n$ random matrix ensembles with their infinite-dimensional, free-probability analogues. Under natural convexity hypotheses, we prove that the non-commutative value function cap...","url_abs":"https://arxiv.org/abs/2511.22804","url_pdf":"https://arxiv.org/pdf/2511.22804v1","authors":"[\"Wilfrid Gangbo\",\"David Jekel\",\"Kyeongsik Nam\",\"Aaron Z. Palmer\"]","published":"2025-11-27T23:28:44Z","proceeding":"math.AP","tasks":"[\"math.AP\",\"math.OA\",\"math.OC\",\"math.PR\"]","methods":"[]","has_code":false}