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Pinning of random directed polymers: smoothening of the transition and some path properties

Monday 9th January 2006 - 16:10 to 17:00
INI Seminar Room 1

I will consider a class of models of directed polymers in interaction with a line of random defects. This includes (d+1)-dimensional pinning problems, the (1+1)--dimensional interface wetting model, random copolymers at selective interfaces and other examples. These models are known to present a (de)localization transition at some critical line in the phase diagram. In absence of disorder, the transition can be either of first or of higher order. I will show that, as soon as disorder is present, the transition is always at least of second order. I will then concentrate on the delocalized phase and discuss some typical properties of the paths. (in collaboration with G. Giacomin (Paris 7))

University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons