The average number of spanning trees in sparse graphs with given degrees

We give an asymptotic expression for the expected number of spanning trees in a random graph with a given degree sequence d=(d1,…,dn), provided that the number of edges is at least n+12dmax4, where dmax is the maximum degree. A key part of our argument involves establishing a concentration result for a certain family of functions over random trees with given degrees, using Prüfer codes.