Sharp asymptotics for the partition function of some continuous-time directed polymers

Agnese Cadel (1, 2) , Samy Tindel (1, 2) , Frederi Viens (3)

1 IECN - Institut Élie Cartan de Nancy
2 TOSCA - Simuler et calibrer des modèles stochastiques
3 Department of Statistics [West Lafayette]

This paper is concerned with two related types of directed polymers in a random medium. The first one is a d-dimensional Brownian motion living in a random environment which is Brownian in time and homogeneous in space. The second is a continuous-time random walk on the lattice Z^d, in a random environment with similar properties as in continuous space. The case of a space-time white noise environment can be acheived in this second setting. By means of some Gaussian tools, we estimate the free energy of these models at low temperature, and give some further information on the strong disorder regime of the objects under consideration.

Mots clés: Polymer model; Random medium; Gaussian field; Free energy

Domaines: Probabilités [math.PR]

Agnese Cadel, Samy Tindel, Frederi Viens. Sharp asymptotics for the partition function of some continuous-time directed polymers. Potential Analysis, 2008, 29, pp.139-166. ⟨10.1007/s11118-008-9092-6⟩. ⟨hal-00176569⟩