Jamie Mingo, Queen's University
"Non-crossing Partitions and the Infinitesimal Law of Real Wishart Random Matrices"
In 1973 G. 't Hooft considered "gauge theory with colour gauge group U(N) and quarks having a colour index from 1 to N''. He showed that in the limit N tends to infinity "only planar diagrams with quarks at the edges dominate''. In 1991 D. Voiculescu showed that, also in the limit N tends to infinity, free probability described the behaviour of independent and unitarily invariant matrix ensembles. In 1994 R. Speicher tied these together when he showed that free independence could be described with non-crossing diagrams.
We introduce a new class of planar diagrams that lie between the non-crossing partitions that connect moments to free cumulants and the annular diagrams used by Nica and Mingo to describe the global fluctuations of random matrices. We show that these diagrams describe the infinitesimal laws for some orthogonally invariant ensembles. The infinitesimal laws discussed here have recently shown up in the work of Arizmendi, Garcia-Vargas, and Perales on the infinitesimal laws of the zeros of some families of orthogonal polynomials.
This is joint work with Josue Vazquez Becerra (UAM Iztapalapa).
Zoom link: https://us02web.zoom.us/j/87274747278?pwd=RG1Bak5lbk1GaHdIL0dtSzlBbjdiUT09