Random Walks Across Dimensions: Exploring Simplicial Complexes (opens in new tab)

arXiv:2601.16086v1 Announce Type: new Abstract: We introduce a novel operator to describe a random walk process on a simplicial complex. Walkers are allowed to wonder across simplices of various dimensions, bridging nodes to edges, and edges to triangles, via a nested organization that hierarchically extends to higher structures of arbitrary large, but finite, dimension. The asymptotic distribution of the walkers provides a natural ranking to gauge the relative importance of higher order sim...