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Explore advanced mathematical concepts in this 43-minute conference talk examining multiplicative Brownian motions on the general linear group. Delve into a family of multiplicative (λ,τ)-Brownian motions parametrized by real variance parameter λ and complex variance parameter τ, and discover the proof that their finite-dimensional marginals converge strongly in the large-N limit to those of free multiplicative (λ,τ)-Brownian motions. Learn about the almost sure convergence properties and gain insights into collaborative research connecting multiplicative stochastic processes, free probability theory, and random matrix theory. Understand the mathematical framework underlying these convergence results and their implications for the study of random matrices and free entropy theory, presented as part of IPAM's specialized workshop on these interconnected mathematical domains.
