AbstractLet be a finite tree. For any matching of , let be the set of vertices uncovered by . Let be a uniform random maximum size matching of . In this paper, we analyze the structure of . We first show that is a determinantal process. We also show that for most vertices of , the process in a small neighborhood of that vertex can be well approximated based on a somewhat larger neighborhood of the same vertex. Then we show that the normalized Shannon entropy of can be also well approximated using the local structure of . In other words, in the realm of trees, the normalized Shannon entropy of —that is, the normalized logarithm of the number of maximum size matchings of —is a Benjamini‐Schramm continuous parameter.