| Identities and Inequalities for Tree Entropy (2008) | |||||||||||||||
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| Abstract. The notion of tree entropy was introduced by the author as a normalized limit of the number of spanning trees in finite graphs, but is defined on random infinite rooted graphs. We give some new expressions for tree entropy and use one of them to prove that tree entropy respects stochastic domination. We also prove that tree entropy is non-negative in the unweighted case. ยง1. Introduction. The enumeration of spanning trees in a finite graph is a classical subject dating to the mid 19th century. Asymptotics began to play a role over 100 years later, in the 1960s. When a sequence of finite graphs converges in an appropriate, but very general, sense, Lyons (2005) gave a formula for the limit of the numbers of spanning trees in that sequence | |||||||||||||||
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