SOME RELATIONS BETWEEN THE SPECTRA OF SIMPLE AND NON-BACKTRACKING RANDOM WALKS

Abstract : 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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Pré-publication, Document de travail
2017
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https://hal.archives-ouvertes.fr/hal-01485495
Contributeur : Nalini Anantharaman <>
Soumis le : mercredi 8 mars 2017 - 21:11:12
Dernière modification le : vendredi 10 mars 2017 - 01:01:55

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170302-Spectral.pdf
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  • HAL Id : hal-01485495, version 1
  • ARXIV : 1703.03852

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Nalini Anantharaman. SOME RELATIONS BETWEEN THE SPECTRA OF SIMPLE AND NON-BACKTRACKING RANDOM WALKS. 2017. <hal-01485495>

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