Relating Entropy and Wasserstein Distance in Free Probability

Explore a 52-minute lecture by David Andrew Jekel from the University of Copenhagen, recorded on April 30, 2025, at IPAM's Dynamics of Density Operators Workshop. Delve into recent advances in developing Wasserstein information geometry for free probability, which aims to describe large-n behavior of Wasserstein information geometry for random matrix models. The presentation focuses on whether displacement concavity of entropy holds in free probability settings and examines if free entropy and free Wasserstein distance represent the large-n limit for matrix models. Discover why certain random matrix models cannot asymptotically realize both entropy and Wasserstein distance simultaneously due to insufficient accounting of interactions with the ambient algebra. Learn about a new framework using continuous model theory that enables reasonable entropy estimates along Wasserstein geodesics. For more information about this UCLA Institute for Pure & Applied Mathematics event, visit the IPAM website.