*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:

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