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Pinning by a Sparse Potential . Janvresse, T. de la Rue and Y. Velenik Stoch. Proc. Appl. 115, No. 8, 1323-1331 (2005). 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. Key words: Polymer, interface, random environment, pinning, localization. Files: PDF, Published version, bibtex