7 papers
Noncommutative -integrators and stochastic differential equations in
David A. Jekel, Todd A. Kemp, Evangelos A. Nikitopoulos
We propose a new framework for noncommutative stochastic integration in , inspired by Bichteler's notion of -integrators, that massively generalizes our previous theory o…
Compact quantum metric spaces from free probability
David Jekel, Therese Basa Landry
We study quantum metric space structures on operator algebras arising from free probability, namely those associated to -Gaussians and free Gibbs laws for convex potentials. We…
Free information geometry and the model theory of noncommutative stochastic processes
David Jekel
We study entropy and optimal transport theory in the free probabilistic setting motivated by the large- theory of random tuples of matrices. We define a new version of free entr…
Large -limit of matrix control problems and non-commutative controls
Wilfrid Gangbo, David Jekel, Kyeongsik Nam +1
Building on the free-probability stochastic control framework introduced in arXiv:2502.17329, we connect optimal control problems for random matrix ensembles with thei…
Viscosity Solutions in Non-commutative Variables
Wilfrid Gangbo, David Jekel, Kyeongsik Nam +1
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…
A martingale approach to noncommutative stochastic calculus
David A. Jekel, Todd A. Kemp, Evangelos A. Nikitopoulos
We present a new approach to noncommutative stochastic calculus that is, like the classical theory, based primarily on the martingale property. Using this approach, we introduce a…
Tracial smooth functions of non-commuting variables and the free Wasserstein manifold
David Jekel, Wuchen Li, Dimitri Shlyakhtenko
We formulate a free probabilistic analog of the Wasserstein manifold on (the formal Riemannian manifold of smooth probability densities on ), and we us…