Matchings on trees and the adjacency matrix: A determinantal viewpoint

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