Семинар Добрушинской математической лаборатории ИППИ РАН
18 июня, вторник, 16:00, ауд. 307.
Frank den Hollander (Leiden University): Spatially extended pinning
Abstract:
We consider a directed polymer interacting with a linear interface. The
monomers carry random charges contributing an energy to the interaction
Hamiltonian that depends on its charge as well as its height with respect
to the interface, modulated by an interaction potential. The configurations
of the polymer are weighted according to the Gibbs measure associated
with the interaction Hamiltonian at a given inverse temperature, where
the reference measure is given by a recurrent Markov chain.
We are interested in both the quenched and the annealed free energy per
monomer in the limit as the polymer becomes large. We find that there is
a phase transition along a critical curve separating a localized phase
(where the polymer stays close to the interface) from a delocalized
phase (where the polymer wanders away from the interface). We obtain
variational formulas for the critical curves, and find that the quenched
phase transition is at least of second order. We obtain upper and lower
bounds on the quenched critical curve in terms of the annealed critical
curve. In addition, for the special case where the reference measure is
given by a Bessel random walk, we identify the weak disorder scaling limit
of the annealed free energy and the annealed critical curve in three
different regimes for the tail exponent of the interaction potential.
Based on joint work with Francesco Caravenna (University of Milano-Bicocca,
Italy).
Архив прошедших семинаров Добрушинской лаборатории
| 14.06.2019 | Комеч Сергей Александрович |