A random matrix and its applications to transportation systems

Abstract

We will construct the probability distribution of eigenvalues of the Hermitian matrices and find the probability that the certain eigenvalues are not in the given compact set, further, we express which in terms of Fredholm determinants, the Painleve equation II, and airy functions. There are many kinds of such density functions and among them particular we will find out how those probability distributions can appear in physical situations, considering bus system models.