How much randomness is needed to prove  a scaling limit result?

In this talk we  consider this question for a family of random walks on the square lattice.

When the randomness is turned to the maximum, we have  the symmetric random walk, which is known to scale to a two-dimensional Brownian motion.

When the randomness is turned to zero,  we have  the rotor walk, for which its scaling limit is an open problem.

This talk is about  random walks that lie in between these two extreme cases and  for which we can prove their scaling limit.

This is a joint work with Lila Greco, Lionel Levine, and Boyao Li.