## Free Probability & Random Matrices Seminar

### Tuesday, March 20th, 2018

**Time:** 3:30-5:00 p.m. **Place:** Jeffery Hall 319

**Speaker:** Mihai Popa (University of Texas, San Antonio)

**Title:** Permutations of Entries and Asymptotic Free Independence for Gaussian Random Matrices

**Abstract: ** Since the 1980's, various classes of random matrices with independent entries were used to approximate free independent random variables. But asymptotic freeness of random matrices can occur without independence of entries: in 2012, in a joint work with James Mingo, we showed the (then) surprising result that unitarily invariant random matrices are asymptotically (second order) free from their transpose. And, in a more recent work, we showed that Wishart random matrices are asymptotically free from some of their partial transposes. The lecture will present a development concerning Gaussian random matrices. More precisely, it will describe a rather large class of permutations of entries that induces asymptotic freeness, suggesting that the results mentioned above are particular cases of a more general theory.