We prove correlation inequalities for linearly edge-reinforced random walk. These correlation inequalities concern the first entry tree, i.e. the tree of edges used to enter any vertex for the first time. They also involve the asymptotic fraction of time spent on particular edges. Basic ingredients are known FKG-type inequalities and known negative associations for determinantal processes.
"Correlation Inequalities for Edge-Reinforced Random Walk." Electron. Commun. Probab. 16 753 - 763, 2011. https://doi.org/10.1214/ECP.v16-1683