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Cumulant-Topological Approaches to Random Matrices

Mathematical Physics & Probability

Speaker: Emily Redelmeier
Location: 2112 MSB
Start time: Fri, Jun 5 2015, 3:00PM

I will discuss topological expansions for multi-matrix expressions, considering the real, complex, and quaternionic cases. Matrix cumulants, developed by Capitaine and Casalis ('06, '07) can be thought of as vertex factors associated with a topological diagram. This approach allows expressions with several independent matrices to be computed in terms of the matrix cumulants of the individual ensembles, which are often simple quantities. I will show how this approach is useful in multi-matrix contexts such as free probability.