Random Matrix Theory Seminars

Matrix-product state (MPS) skeletons are connected networks of local one-dimensional quantum lattice models with ground states admitting an MPS representation with finite bond dimension. In this talk, I will discuss how such skeletons underlie certain families of models obeying the Onsager algebra, and how these simple ground states provide a route to explicitly computing correlation functions.

I'll discuss some of the history of the use of random matrices for studying the structure of operator algebras, starting with Voiculescu's notion free independence. We'll see that the original notions of convergence of random matrix models to certain infinite-dimensional operators is actually fairly weak, and discuss the more recent "strong convergence" phenomenon and its applications to C*-algebras. Finally, I'll touch upon some ongoing work, joint with A. Shiner and S. White, for continuing to use random matrix tools to prove structural properties of C*-algebras.