On end-point distribution for directed polymers and related problems for randomly forced Burgers equation

In this paper, we study several problems related to the theory of randomly forced Burgers equation. Our numerical analysis indicates that despite the localization effects the quenched variance of the endpoint distribution for directed polymers in the strong disorder regime grows as the polymer length t ->infinity. We also present numerical results in support of the 'one force-one solution' principle. This article is part of the theme issue 'Scaling the turbulence edifice (part 2)'.