Pólya urns on hypergraphs

Abstract

We study Pólya urns on hypergraphs and prove that, when the incidence matrix of the hypergraph is injective, there exists a point $v=v(H)$ such that the random process converges to $v$ almost surely. We also provide a partial result when the incidence matrix is not injective.

20 pages, 2 figures, to appear in Nonlinearity