Consider the random circle rotation $x \to x + Z \text{ mod 1}$ on the unit circle, where at each rotation, $Z$ is uniformly distributed on $[0, 1]$ and independent of previous rotations.

Is it true that almost surely, the system is weak mixing?

Remark: Note that the rotation by a fixed number is never weak mixing due to being an isometric system.

Consider the random circle rotation $x \to x + Z \text{ mod 1}$ on $([0, 1], \text{Lebesgue})$ where at each rotation, $Z$ is uniformly distributed on $[0, 1]$ and independent of previous rotations.

Is it true that almost surely, the system is weak mixing?

Remark: Note that the rotation by a fixed number is never weak mixing due to being an isometric system.