Pinning by a sparse potential
  We consider a directed polymer interacting with a diluted pinning potential restricted to a line. We characterize explicitely the set of disorder configurations that give rise to localization of the polymer. We study both relevant cases of dimension 1+1 and 1+2. We also discuss the case of massless effective interface models in dimension 2+1. 
\'Elise Janvresse (LMRS), Thierry De La Rue (LMRS), Yvan Velenik   (LMRS)