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This lecture presents "The Airy-beta line ensemble" by Vadim Gorin from the University of California, Berkeley, delivered at IPAM's Free Entropy Theory and Random Matrices Workshop on February 27, 2025. Explore beta-ensembles that generalize eigenvalue distributions of self-adjoint real, complex, and quaternion matrices for beta=1,2, and 4, respectively. Discover how these ensembles extend to two dimensions through operations like corner truncation, addition, or multiplication of matrices. Learn about the edge asymptotics of two-dimensional ensembles and the Airy-beta line ensemble—a universal object governing the asymptotics of time-evolving largest eigenvalues. Understand this remarkable structure consisting of an infinite collection of continuous random curves parameterized by beta, and gain insights into recent framework developments for describing it. The 38-minute talk was recorded at UCLA's Institute for Pure & Applied Mathematics.
