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- W2155748440 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; one uses Fuglede–Kadison determinants, while another uses effective resistance. We use the latter to prove that tree entropy respects stochastic domination. We also prove that tree entropy is non-negative in the unweighted case, a special case of which establishes Lück's Determinant Conjecture for Cayley-graph Laplacians. We use techniques from the theory of operators affiliated to von Neumann algebras." @default.
- W2155748440 created "2016-06-24" @default.
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- W2155748440 date "2009-12-15" @default.
- W2155748440 modified "2023-09-23" @default.
- W2155748440 title "Identities and Inequalities for Tree Entropy" @default.
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- W2155748440 doi "https://doi.org/10.1017/s0963548309990605" @default.
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