Events for 02/03/2023 from all calendars

Mathematical Physics and Harmonic Analysis Seminar

Time: 1:50PM - 2:50PM

Location: BLOC 302

Speaker: Patricia Ning, TAMU

Title: Mosco Convergence of Dirichlet Forms on Machine Learning Gibbs Measures

Abstract: The Metropolis-Hastings (MH) algorithm as the most classical MCMC algorithm, has had a great influence on the development and practice of science and engineering. The behavior of the MH algorithm in high-dimensional problems is typically investigated through a weak convergence result of diffusion processes. In this paper, we introduce Mosco convergence of Dirichlet forms in analyzing the MH algorithm on large graphs, whose target distribution is the Gibbs measure that includes any probability measure satisfying a Markov property. The abstract and powerful theory of Dirichlet forms allows us to work directly and naturally on the infinite-dimensional space, and our notion of Mosco convergence allows Dirichlet forms associated with the MH Markov chains to lie on changing Hilbert spaces. Through the optimal scaling problem, we demonstrate the impressive strengths of the Dirichlet form approach over the standard diffusion approach.

Free Probability and Operators

Time: 4:00PM - 5:00PM

Location: BLOC 306

Speaker: Ken Dykema, TAMU

Title: On spectral and decomposable operators in finite von Neumann algebras. (cont.)

Abstract: We describe spectral and decomposable operators on Hilbert spaces and then, in the case of operators belonging to finite von Neumann algebras, relate these properties to the Haagerup-Schultz subspaces of the operators. Finally, we will examine certain such operators arising naturally in free probability theory.