I am going to talk about a continuum model of directed polymer in random environment. The law of the polymer is defined as the Brownian motion conditioned to survive among space-time Poissonian disasters. This model is well-studied in the positive temperature regime. However, at zero-temperature, even the existence of the free energy has not been proved. Stefan Junk and I have proved that the free energy exists and is continuous at zero-temperature.
Dernière modification le 7 Mars 2017