The Spectra of Infinite Hypertrees
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  • Abstract:

    We develop a model of regular, infinite hypertrees, to mimic for hypergraphs what infinite trees do for graphs. We then examine two notions of spectra or ``first eigenvalue'' 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.