In an empirical study of a two-sided large matching market (such as a college admissions problem), the primary statistics of interest are often the empirical matching probabilities which represent the fraction of students of a given type who match with colleges of a given type. This paper studies the concentration-of-measure phenomenon for the empirical matching probabilities  when the matching is generated from a student-optimal stable matching mechanism. We introduce a notion of partial homogeneity of preferences to express the degree of alignment in the preferences 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.
In an empirical study of a two-sided large matching market (such as a college admissions problem), the primary statistics of interest are often the empirical matching probabilities which represent the fraction of students of a given type who match with colleges of a given type. This paper studies the concentration-of-measure phenomenon for the empirical matching probabilities and related statistics when the matching is generated from a student-optimal stable matching mechanism. We introduce a notion of partial homogeneity of preferences to express the degree of alignment in the preferences of colleges over students, and show that the more the preferences are aligned, the more the empirical 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.
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and related statistics
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empirical