Eigenvalue distribution of nonlinear models of random matrices

Understand

This paper is concerned with the asymptotic empirical eigenvalue distribution of a non linear random matrix ensemble.

• More precisely we consider $M= \frac{1}{m} YY^*$ with $Y=f(WX)$ where $W$ and $X$ are random rectangular matrices with i.i.d.
• centered entries.
• The function $f$ is applied pointwise and can be seen as an activation function in (random) neural networks.