The totally asymmetric simple exclusion process (TASEP) is a simple but fundamental model of particle systems. It can be thought of as a simple traffic model. It was shown in 2000 that one point fluctuations of TASEP in 1+1 dimensions for certain initial conditions are given by the same distribution function occurring in random matrix theory. This result was obtained from a remarkable Fredholm determinant formula of the marginal distribution. We will discuss a proof of this Fredholm determinant formula using the so-called coordinate Bethe ansatz method developed by Schutz, Rakos, Tracy, and Widom. Speaker(s): Jinho Baik (University of Michigan)