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Random walk on simplicial complexes

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Random walk on simplicial complexes
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19
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CC Attribution - NonCommercial - NoDerivatives 4.0 International:
You are free to use, copy, distribute and transmit the work or content in unchanged form for any legal and non-commercial purpose as long as the work is attributed to the author in the manner specified by the author or licensor.
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Abstract
We generalize random walks on graphs to random walks on simplicial complexes, also called hypergraphs, using some notions of topological algebra. The transition matrix of this RW is related to the higher order Laplacian which is the generalization of graph Laplacian. We also analyze the limit behavior of this RW when the number of points in the simplicial complex tends to infinity.