## Spectra of Random Hypergraphs and the Symmetric Bernoulli Hyperensemble

- Aug. 31, 2015
- 3:30 p.m.
- LeConte 312

## Abstract

We present progress towards an asymptotic understanding of the adjacency spectra of an (Erdos-Renyi) random hypergraph, which is conjectured to be (with high probability) a scaled and slightly perturbed copy of the spectrum of the all-ones hypermatrix. In particular, we show that a random symmetric +/-1 hypermatrix has small spectral radius, of order O(n^{(k-1)/2}), using large deviation inequalities and epsilon-nets. Since this radius is proportional to that of the residual when an appropriate rank-one hypermatrix is subtracted from the adjacency hypermatrix of a random hypergraph, a natural Weyl-type inequality would yield the aforementioned conjecture.