Probability Seminar

Speaker: Quentin Berger (USC)

Title: The critical curve of the Copolymer Model at weak coupling

Abstract: We will present the Copolymer Model introduced by Sinai, used to describe a heteregeneous polymer chain (say composed of hydrophilic or lipophilic monomers) lying at the interface between two solvents (say water and oil). When increasing the temperature, one observes a localization/delocalization phase transition: at low temperature, the polymer stays close to the interface to maximize the matches, whereas at high temperature, it wanders in one of the two solvents. We focus here on the critical curve, that separates the two regimes in this phase transition. In particular, we study its weak coupling limit, which is known to be universal. The value of the limit has however been subject to discussions, leading to contradictory conjectures. The result we will present is that we are actually able to compute the limit, under the assumption that the underlying return distribution has a power-law tail with finite mean. (joint work with F. Caravenna, J. Poisat, R. Sun, N. Zygouras)