Width of handles in two-dimensional quantum gravity

We discuss the average length l̄ of the shortest non-contractible loop on surfaces in the two-dimensional pure quantum gravity ensemble. The value of γstr and the explicit form of the continuum loop functions indicate that l̄ diverges at the critical point. Scaling arguments suggest that the critical exponent of l̄ is 12. We show that this value of the critical exponent is also obtained for branched polymers with loops where the calculation is straightforward.