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A model of regular infinite hypertrees is developed to mimic for hypergraphs what infinite trees do for graphs. Two notions of spectra, or “first eigenvalue,” are then examined for the infinite tree, obtaining a precise value for the first notion and obtaining some estimates for the second. The results indicate agreement of the first eigenvalue of the infinite hypertree with the ”second eigenvalue“ of a random hypergraph of the same degree, to within logarithmic factors, at least for the first notion of first eigenvalue.
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Joel Friedman (1991) studied this question.
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