  In this paper, we introduce random walks with absorbing states on simplicial
complexes. Given a simplicial complex of dimension $d$, a random walk with an
absorbing state is defined which relates to the spectrum of the $k$-dimensional
Laplacian for $1 \leq k \leq d$ and which relates to the local random walk on a
graph defined by Fan Chung. We also examine an application of random walks on
simplicial complexes to a semi-supervised learning problem. Specifically, we
consider a label propagation algorithm on oriented edges, which applies to a
generalization of the partially labelled classification problem on graphs.
