CRM: Centro De Giorgi
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Stochastic Analysis, Stochastic Partial Differential Equations and Applications to Fluid Dynamics and Particle Systems

seminar: A renewal theory approach to weakly inhomogeneous polymer models

speaker: Francesco Caravenna (Università degli Studi di Milano-Bicocca)

abstract: (Joint work with G. Giacomin and L. Zambotti)

We consider a probabilistic model of an heterogeneous polymer chain fluctuating in the proximity of an interface between two selective solvents. The heterogeneous character of the model comes from the fact that each monomer unit interacts with the solvents and with the interface according to some "charge" that it carries. In this talk we focus on the so-called weakly inhomogeneous case, when the charges repeat themselves along the chain in a periodic fashion. The main question on this model is whether the polymer remains tightly close to the interface, a phenomenon called localization, or there is a marked preference for one of the two solvents yielding thus a delocalization phenomenon. We present an approach based on renewal theory that allows to get a complete understanding of the localizationdelocalization issue, yielding a precise pathwise description of the polymer measure both in a local sense thermodynamic limit) and in a global sense (scaling limits). Analogous results can be obtained also in the context of (1+1)-dimensional interface wetting models, where the same approach is applicable.

Tue 6 Jun, 16:30 - 17:00, Aula Mancini
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