Multifractal spectra and precise rates of decay in homogeneous   fragmentation
  We consider a mass-conservative fragmentation of the unit interval. The main purpose of this work is to specify the Hausdorff dimension of the set of locations having exactly an exponential decay. The study relies on an additive martingale which arises naturally in this setting, and a class of L\'evy processes constrained to stay in a finite interval. 
Nathalie Krell (PMA)