Hausdorff dimension of images and graphs of some random complex series

Chun-Kit Lai, Ka-Sing Lau, Peng-Fei Zhang

Let $\{X_n=e^{2\ddot{I}€i\hat{I}{¸}_n}\}$ be a sequence of Steinhaus random variables, where $\hat{I}{¸}_n$ are independent and uniformly distributed on $[0,1]$. We compute the almost sure Hausdorff di…