This project involves the study of current fluctuations in the
asymmetric simple exclusion process for a variety of initial
configurations. This is a model of interacting particles on a
one-dimensional lattice. The model has attracted wide attention from
both mathematicians and physicists since it is one of the simplest
models to incorporate far from equilibrium behavior with nonclassical
fluctuations. These fluctuations are expected to have a new universal
behavior similar in their applicability to the famous bell-shaped
curve (the Gaussian distribution) of classical probability. A
long-term goal of research in this area is the establishment of new
limit laws similar in nature to the classical central limit theorem.
Already these new universal distributions are being applied to various
problems in growth processes, population genetics, and finance. This
project will extend our knowledge of fluctuations to a much wider
class of growth models.