  We describe the first known mean-field study of landing probabilities for
random walks on hypergraphs. In particular, we examine clique-expansion and
tensor methods and evaluate their mean-field characteristics over a class of
random hypergraph models for the purpose of seed-set community expansion. We
describe parameter regimes in which the two methods outperform each other and
propose a hybrid expansion method that uses partial clique-expansion to reduce
the projection distortion and low-complexity tensor methods applied directly on
the partially expanded hypergraphs.
