  In many empirical studies of a large two-sided matching market (such as in a
college admissions problem), the researcher performs statistical inference
under the assumption that they observe a random sample from a large matching
market. In this paper, we consider a setting in which the researcher observes
either all or a nontrivial fraction of outcomes from a stable matching. We
establish a concentration inequality for empirical matching probabilities
assuming strong correlation among the colleges' preferences while allowing
students' preferences to be fully heterogeneous. Our concentration inequality
yields laws of large numbers for the empirical matching probabilities and other
statistics commonly used in empirical analyses of a large matching market. To
illustrate the usefulness of our concentration inequality, we prove consistency
for estimators of conditional matching probabilities and measures of positive
assortative matching.
