Niveau: Supérieur, Doctorat, Bac+8
Sharp asymptotics for the partition function of some continuous-time directed polymers Agnese Cadel Samy Tindel Institut Elie Cartan, Universite de Nancy 1 BP 239, 54506-Vandoeuvre-les-Nancy, France [cadel,tindel]@iecn.u-nancy.fr Frederi Viens ? Dept. Statistics & Dept. Mathematics, Purdue University 150 N. University St., West Lafayette, IN 47907-2067, USA August 29, 2007 Abstract 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 en- vironment which is Brownian in time and homogeneous in space. The second is a continuous-time random walk on Zd, in a random environment with similar properties as in continuous space, albeit defined only on R+?Zd. 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. Key words and phrases: Polymer model, Random medium, Gaussian field, Free energy. MSC: 82D60, 60K37, 60G15. ?This author's research partially supported by NSF grant no.
- disorder regime
- change over
- brownian polymer
- gaussian field
- article can
- brownian
- continuous space
- over time
- time random