Restrictions of Brownian motion

Richárd Balka, Yuval Peres

Let $\{B(t):0\le t\le 1\}$ be a linear Brownian motion and let $\dim$ denote the Hausdorff dimension. Let $\alpha >\frac{1}{2}$ and $1\le \beta \le 2$. We prove that, almost surely, t…