We consider two dimensional standard brownian motion $B: t\mapsto (B_{1}(t),B_{2}(t))$. Let $D$ be its range (that is the image of $[0,+\infty[$ by $B$ i.e, $B([0,+\infty[)$).
Is there some known results about the value of the Hausdorff dimension of the intersection of the range with a line ?