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arXiv · 2511.22804

Large $n$-limit of matrix control problems and non-commutative controls

Wilfrid Gangbo·David Jekel·Kyeongsik Nam·Aaron Z. Palmer
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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.

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Wilfrid Gangbo, David Jekel, Kyeongsik Nam, Aaron Z. Palmer. 2025-11-27. Large $n$-limit of matrix control problems and non-commutative controls. https://arxiv.org/abs/2511.22804

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