Intersection Local Time for Points of Infinite Multiplicity

Abstract

For each $a \in (0, \frac{1}{2})$, there exists a random measure $\beta_a$ which is supported on the set of points where two-dimensional Brownian motion spends $a$ units of local time. The measure $\beta_a$ is carried by a set which has Hausdorff dimension equal to $2 - a$. A Palm measure interpretation of $\beta_a$ is given.