arXiv subjects

Aaron Z. Palmer

Publications and source records attributed to Aaron Z. Palmer.

3 recordsLinked to original sources

arXiv2025

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

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.

math.AP↗

arXiv2025

Viscosity Solutions in Non-commutative Variables

Motivated by parallels between mean field games and random matrix theory, we develop stochastic optimal control problems and viscosity solutions to Hamilton-Jacobi equations in the setting of non-commutative variables. Rather than real vectors, the inputs to the equation are tuples of self-adjoint operators from a tracial von Neumann algebra. The individual noise from mean field games is replaced by a free semi-circular Brownian motion, which describes the large-$n$ limit of Brownian motion on the space of self-adjoint matrices. We introduce a classical common noise from mean field games into the non-commutative setting as well, allowing the problems to combine both classical and non-commutative randomness.

math.AP↗

arXiv2021

Optimal control of COVID-19 infection rate considering social costs

The COVID-19 pandemic has posed a policy making crisis where efforts to slow down or end the pandemic conflict with economic priorities. This paper provides mathematical analysis of optimal disease control policies with idealized compartmental models for disease propagation and simplistic models of social and economic costs. Two locally optimal control strategies are found and categorized as `suppression' and `mitigation' strategies. We analyze how these strategies change when we incorporate vaccination into the model and find a new optimal `delay-mitigation' strategy.

math.OC↗