A stable matching between two sets of agents (such as students and colleges) has received a great deal of attention in the literature. For an empirical study of matching markets, the main statistics of interest are  the matching frequencies, which show the fraction of students of a given type who match with colleges of a given type. We study the concentration-of-measure phenomenon for  matching frequencies when the observed matching is generated from a Deferred Acceptance algorithm . 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 .
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 .
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A stable matching between two sets of agents (such as students and colleges) has received a great deal of attention in the literature. For
In
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matching markets, the main
a two-sided large matching market (such as a college admissions problem), the primary
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often the empirical matching probabilities which represent
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matching frequencies, which show the
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We study
This paper studies
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the empirical matching probabilities when the
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frequencies when the observed matching
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Deferred Acceptance algorithm
student-optimal stable matching mechanism
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correlated priorities of
the degree of alignment in the preferences of
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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
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