Description
Directed polymers in a singular fractional environment: well-posedness and free-energy asymptotics
Directed polymers in random environments describe paths which are subject to competition between entropy, which favours diffusion, against the energy of a random, disordered medium, which favours localisation. After a brief word on polymer models in continuous space-time media, I will turn to environments that are irregular and long-range correlated, modelled by a space-time fractional Gaussian noise which is too rough for path-by-path integration. I will explain how to give meaning to the Hamiltonian and the polymer measure, and then describe the long-time behaviour of the free energy, leading to the conclusion that this polymer is subject to strong disorder.
Joint work with Julien Enguehard.