Séminaire SPACE Tours

Collapse transition and geometry of a self-interacting partially directed random walk
Nicolas Pétrélis (Laboratoire Jean Leray, Université de Nantes)
Friday 18 April 2014 11:00 -  Tours -  Salle 1180 (Bât E2)

Résumé :
In this talk, we will consider a model for a $1+1$ dimensional self-interacting and partially directed self-avoiding walk, usually referred to as IPDSAW. The IPDSAW is known to undergo a collapse transition at some critical temperature and had been studied until recently with combinatorics techniques exclusively. We will present here a new method that provides a probabilistic representation of the partition function and allows us to push forward the investigation of the model. For instance, we will provide the precise asymptotic of the free energy close to criticality and we will establish some path properties of the random walk inside the collapsed phase, that is we will show that the geometric conformation adopted by the polymer is made of a succession of long vertical stretches that attract each other to form a unique macroscopic bead, whose upper and lower envelopes, once properly rescalled, converge to a deterministice Wulff shape.

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