title: Random walks on simplicial complexes and harmonics.
abstract: In this paper, we introduce a class of random walks with absorbing states on simplicial complexes. Given a simplicial complex of dimensiond, a random walk with an absorbing state is defined which relates to the spectrum of thek-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.
authors.affiliation: Departments of Statistical Science, Mathematics and Computer Science Duke University.
authors.forename: Sayan
authors.initials: S
authors.lastname: Mukherjee
authors.affiliation: Department of Mathematics University of Illinois at Chicago.
authors.forename: John
authors.initials: J
authors.lastname: Steenbergen
keywords: random walks; simplicial complexes; spectral theory