Zeros and Critical Points of Random Polynomials

Inspired by Boris Hanin's paper   Pairing of Zeros and Critical Points for Random Polynomials
where it is proved that critical points cluster near to the roots,
this app computes and plots the zeros and critical points of random polynomials:
\( \quad f(z) = \displaystyle \sum_{j = 0}^n \alpha_j \; z^j \)   where   \( \alpha_j \) are independent Cauchy and N(0,1) random variables.

Provide the degree of the polynomial:       n =     and click     Compute

Select how many polynomials:       numpoly =

The orange dots are the zeros and the blue dots are the critical points.

Updated 2023 Oct 28