Stochastic matrix description of the glass transition

We present a model of the glass transition viewed as the agglomeration and growth of clusters forming a covalent network. The creation of new layers o f atoms on the rims of the clusters is treated in a probabilistic way as a linear transformation (encoded in what is called a stochastic matrix) of a vector whose components represent the probability distribution of various s ites found on the rim. The asymptotic limit of the statistics of sites in t he network is given by the matrix eigenvector with eigenvalue equal to one. The model reproduces the modified Gibbs-DiMarzio equation with a system pa rameter that is comparable to the one observed experimentally for many chal cogenide glasses. Some other features of the glass transition process, like the form of the specific heat, are also obtained.