  It has been known for a few years that the occupation measure of several
models of embedded trees converges, after a suitable normalization, to the
random measure called ISE (Integrated SuperBrownian Excursion). Here, we prove
a local version of this result: ISE has a (random) H\"{o}lder continuous
density, and the vertical profile of embedded trees converges to this density,
at least for some such trees. As a consequence, we derive a formula for the
distribution of the density of ISE at a given point. This follows from earlier
results by Bousquet-M\'{e}lou on convergence of the vertical profile at a fixed
point. We also provide a recurrence relation defining the moments of the
(random) moments of ISE.
