Tracy and Widom found a new type of probability distribution in
the study of high dimensional random matrices in the 1990s, which is nowadays normally
called Tracy-Widom distribution. It is used to described the limiting distribution of the
extremal eigenvalues in Gaussian Unitary Ensemble. Later on, the study in the past two
decades indicates that Tracy-Widom distribution is universal like normal distribution and
can be well used to describe a lot of seemingly distinct random phenomena. As illustrations,
the paper briefly review nine widely studied random models, each of which is more or
less related to Tracy-Widom distribution. Compared to normal distribution, Tracy-Widom
distribution has horribly intricate distribution function, density function and moments.
people need to use deep mathematical knowledge and advanced computation technology in order
to extend and to apply Tracy-Widom distribution in practice. But it is absolutely worthy
further study on account of its importance.