The Spectra of Infinite Hypertrees
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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.