Recorded 25 February 2025. Ping Zhong of the University of Houston presents "Limiting Eigenvalue Distribution and Outliers of Deformed Single Ring Random Matrices" at IPAM's Free Entropy Theory and Random Matrices Workshop. Abstract: We consider a square random matrix of the form A + Y, where A is deterministic and Y is invariant under the left and right actions of the unitary group. Then single ring theorem (due to Guionnet, Krishnapur and Zeitouni) says that the eigenvalue distribution of Y converges to the Brown measure of a R-diagonal operator T. Under certain conditions, we show that the eigenvalue distribution of A+Y converges weakly to the Brown measure of the operator a+T, where represents the limit of A. If A has some eigenvalues outside of the support of the limit probability measure, we show that A+Y may or may not produce outliers in some neighborhood of these eigenvalues of A, depending on their locations. This result extends a work of Benaych-Georges and Rochet for the case when A has a finite rank. Joint works with Hari Bercovici, Ching-Wei Ho, and Zhi Yin. Learn more online at: https://www.ipam.ucla.edu/programs/workshops/free-entropy-theory-and-random-matrices/