Before revision:  We introduce a notion of partial homogeneity of preferences to express correlated priorities of colleges over students, and demonstrate the relation between partial homogeneity and concentration of measure. Our concentration inequality immediately yields the rate of convergence for the law of large numbers for matching frequencies .
After revision:  We introduce a notion of partial homogeneity of preferences to express correlated priorities of colleges over students, and show that the more the preferences are aligned, the more the matching frequencies tend to concentrate on their expected value given the colleges' types. This means that the empirical matching probabilities become more robust to realizations of students' preferences when the colleges' preferences are more aligned .