Janowsky Steven A., Lebowitz Joel L. Finite Size Effects and Shock Fluctuations in the Asymmetric Simple Exclusion Proces (177K, LaTeX) ABSTRACT. We consider a system of particles on a lattice of $L$ sites, set on a circle, evolving according to the asymmetric simple exclusion process, {\em i.e.}\ particles jump independently to empty neighboring sites on the right (left) with rate $p$ (rate $1-p$), $1/2