Yashar will be presenting preliminary work on applying random matrix theory to the study of transient dynamics in a non-normal linear neural network.
The project is a collaboration with Ken Miller, and is motivated by his work on non-normal dynamics and transient amplification due to non-normality. I will give a brief background on this work
(see this paper: Balanced amplification: a new mechanism of selective amplification of neural activity patterns, by B.K. Murphy and K.D. Miller), and then give an expose of the diagrammatic method for calculating averages over a random (Hermitian N x N) matrix ensemble in the large N limit.
As an example, I will present how to derive the semi-circular law for Gaussian Hermitian matrices.
Finally, I will discuss how one can extend the method to cover the non-normal case, and I will derive a formula for the spectral density in the large N limit.