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Some relations between the spectra of simple and non-backtracking random walks

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arxiv 1703.03852 v1 pith:NI5HRDUQ submitted 2017-03-09 math.PR

classification math.PR
keywords randomnon-backtrackingsimplesomewalkdeterminantgraphsrelations
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We establish some relations between the spectra of simple and non-backtracking random walks on non-regular graphs, generalizing some well-known facts for regular graphs. Our two main results are 1) a quantitative relation between the mixing rates of the simple random walk and of the non-backtracking random walk 2) a variant of the "Ihara determinant formula" which expresses the characteristic polynomial of the adjacency matrix, or of the laplacian, as the determinant of a certain non-backtracking random walk with holomorphic weights.

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  1. On discrete loop signatures and Markov loops topology

    math.PR 2019-08 conditional novelty 6.0 of 10

    For Markov loop ensembles on finite graphs, the paper obtains the joint distribution of the second homology of loops, expressed through a limit of determinants via nilpotent holonomy.

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