Polímeros orientados em ambientes aleatórios - Larissa Brito de Oliveira (2011)
The main purpose of the present dissertation is the study of directed polymers in a random environment on Z^d, based on the article "Probabilistic Analysis of Directed Polymers in a Random Environment: a Review" by F. Comets, T. Shiga e N. Yoshida, published in 2004. We will study the difusive behavior on the so-called weak disorder phase and the localized behavior on the so-called strong disorder phase. The results on the weak disorder were originally obtained by J. Imbrie and T. Spencer in 1988 and by E. Bolthausen in 1989, while the results on strong disorder were proved by P. Carmona e Y. Hu in 2002 and by F. Comets, T. Shiga and N. Yoshida in 2003.Moreover, the phase transition of the free energy will be established for the directed polymer model on the regular Cayley tree. This result is based on the article "Directed polymers on trees: a martingale approach" de E. Buffet, A. Patrick and J. V. Pulé, published in 1993.