Random walks on simplicial complexes and harmonics1. Issue 2 (7th March 2016) - Mukherjee, Sayan; Steenbergen, John
Abstract: In this paper, we introduce a class of 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 ≤  k  ≤  d . We study an example of random walks on simplicial complexes in the context of 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. © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 49, 379–405, 2016