2015/07/25 by Joshua Cooper, Cooper, Joshua · 1 citation
Computer Science · Mathematics · #Graph theory and applications #Matrix Theory and Algorithms #Tensor decomposition and applications #acm:05C65 #acm:05C80 #acm:60B20 #math.CO #msc:05C65 #msc:05C80 #msc:60B20
paper · pdf · doi:10.48550/arxiv.1507.07118
22 pages, no figures
arxiv created 2018/01/08 · arxiv updated 2018/01/10
We present progress on the problem of asymptotically describing the adjacency eigenvalues of random and complete uniform hypergraphs. There is a natural conjecture arising from analogy with random matrix theory that connects these spectra to that of the all-ones hypermatrix. Several of the ingredients along a possible path to this conjecture are established, and may be of independent interest in spectral hypergraph/hypermatrix theory. In particular, we provide a bound on the spectral radius of the symmetric Bernoulli hyperensemble, and show that the spectrum of the complete \(k\)-uniform hypergraph for \(k=2,3\) is close to that of an appropriately scaled all-ones hypermatrix.