Brownian Directed Polymers in Random Environment

Abstract: Joint work with Nobuo Yoshida. We study the thermodynamics of a continuous model of directed polymers in random environment. The environment is given by a space-time Poisson point process, whereas the polymer is defined in terms of the Brownian motion. We mainly discuss:

1. The phase diagram, based on the free energy
2. Positivity of the limiting partition function and some natural localization properties of the path.
3. The almost sure large deviation principle for the polymer measure.

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