Sidorenko-type inequality for determinants

We study a class of determinant inequalities that are closely related to Sidorenko's famous conjecture (also conjectured by Erdős and Simonovits in a different form). Our main result can also be interpreted as an entropy inequality for Gaussian Markov random fields. Connection with graph homomorphisms, Ihara zeta function and the number of spanning trees is also discussed. Joint work with Balázs Szegedy.