Resumo: In this talk I will introduce the weakly asymmetric simple exclusion process in the one dimensional lattice. In this process each particle waits an exponential random time after which, jumps to one of the neighboring sites. The probability of jumping to the right is slightly bigger that the probability of jumping to the left, so that the system is weakly asymmetric. In this talk I will expose some results on the equilibrium fluctuations for this process by exhibiting a phase transition that goes from the Edwards-Wilkinson (EW) universality class to the Kardar-Parisi-Zhang (KPZ) universality class. This phase transition depends on the strenght of the asymmetry which is given by $n^{2-\gamma}$. For $\gamma>1/2$ the system falls into the EW class and for $gamma=1/2$ it falls into the KPZ class. I will present the extension of this result to a general class of one-dimensional models.
Trabalho conjunto com Milton Jara (IMPA).