Root-to-leaf path random walks on double covers of graded signed graphs normalize the Hodge Laplacian on simplicial complexes and yield Cheeger inequalities for the upper spectrum.
Difference Equations, Isoperimetric Inequality and Transience of Certain Random Walks.Transactions of the American Mathematical Society, 284(2):787–794
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Root-to-Leaf Path Random Walks, Normalized Hodge Laplacians, and Cheeger Inequalities on Simplicial Complexes
Root-to-leaf path random walks on double covers of graded signed graphs normalize the Hodge Laplacian on simplicial complexes and yield Cheeger inequalities for the upper spectrum.