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

Nalini Anantharaman (1)

1 IRMA - Institut de Recherche Mathématique Avancée

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.

Mots clés: Spectral graph theory

Domaines: Mathématiques générales [math.GM]

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