For a sufficiently nice 2-dimensional shape, we define its approximating matrix (or patterned matrix) as a random matrix with iid entries arranged according to the given pattern. For large approximating matrices, we observe that the eigenvalues roughly follow an underlying distribution. This phenomenon is similar to the classical observation on Wigner matrices. We prove that the moments of such matrices converge asymptotically as the size increases and equals to the integral of a combinatorially-defined function which counts certain paths on a finite grid.

**ASUERAU C*-Seminar
November 23, 2022
WXLR A307 and Virtual via Zoom
1:30-2:45pm MST/AZ**

Our C*-Seminar will again be on Wednesdays from 1:30-2:45 pm (Arizona time, no daylight savings), meeting both in person (WXLR A307) and via zoom.

Also new: it's now the ASUERAU C*-Seminar (so, joint with our friends Lara and Mitch at Embry-Riddle Aeronautical University up the road in Prescott).

(Please email the organizer John Quigg quigg@asu.edu to be put on the email list if you would like to receive the link to the zoom seminar.)

Tapesh Yadav

University of Florida