We study coupled random walks in the plane such that, at each step, the walks change direction by a uniform random angle plus an extra deterministic angle $\theta$. We compute the Hausdorff dimension of the $\theta$ for which the walk has an unusual behavior. This model is related to a study of the spectral measure of some random matrices. The same techniques allow to study the boundary behavior of some Gaussian analytic functions.
"Random walks veering left." Electron. J. Probab. 18 1 - 25, 2013. https://doi.org/10.1214/EJP.v18-2523