Student Probability and Mathematical Physics Seminar

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Introduction to Free Independence (and why you might care about it)

Speaker: Benjamin Eisley, CIMS

Location: Warren Weaver Hall 202

Date: Tuesday, November 11, 2025, 12:30 p.m.

Synopsis:

Traditional probability assumes that we can observe random variables without changing the state of our system. If we instead treat our random variables as experiments which may interact with one another, we discover noncommutative probability. There is a natural notion of independence in this context, free independence, which does not agree with our usual notion of independence. I will introduce free independence, and argue that this is the correct notion for large random matrices by proving that independent Gaussian Unitary Ensembles converge as their width go to infinity to freely independent noncommutative random variables.