Asymptotic Enumeration of Spanning Trees
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Publication:5696361
DOI10.1017/S096354830500684XzbMATH Open1076.05007arXivmath/0212165OpenAlexW2061309095WikidataQ105583884 ScholiaQ105583884MaRDI QIDQ5696361
Author name not available (Why is that?)
Publication date: 18 October 2005
Published in: (Search for Journal in Brave)
Abstract: We give new general formulas for the asymptotics of the number of spanning trees of a large graph. A special case answers a question of McKay (1983) for regular graphs. The general answer involves a quantity for infinite graphs that we call "tree entropy", which we show is a logarithm of a normalized determinant of the graph Laplacian for infinite graphs. Tree entropy is also expressed using random walks. We relate tree entropy to the metric entropy of the uniform spanning forest process on quasi-transitive amenable graphs, extending a result of Burton and Pemantle (1993).
Full work available at URL: https://arxiv.org/abs/math/0212165
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