Recent questions showed that roots of a random polynomial tend to lie on the unit circle ("Why do roots of polynomials tend to have absolute value close to 1?"; "Distribution of roots of complex polynomials").
I wonder if this fact can be somehow seen as a consequence of (or at least related to) Gromov's waist theorem? Can Andrej Bauer's image be viewed as a projection to the plane of a sphere whose waist is dense in roots?
