Asymptotic Spectral Distributions of Distance k-Graphs of Cartesian Product Graphs

2013/04/04 by Yuji Hibino, Hibino, Yuji, Hun Hee Lee +3
Mathematics · #47A10 #81S25 #FOS: Mathematics #Functional Analysis (math.FA) #Graph theory and applications #Markov Chains and Monte Carlo Methods #Primary 05C50 #Probability (math.PR) #Random Matrices and Applications #Secondary 05C12

paper · pdf · doi:10.48550/arxiv.1304.1236

openalex publication_date 2013/04/04 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

Let G be a finite connected graph on two or more vertices and G^[N,k] the distance k-graph of the N-fold Cartesian power of G. For a fixed k≥1, we obtain explicitly the large N limit of the spectral distribution (the eigenvalue distribution of the adjacency matrix) of G^[N,k]. The limit distribution is described in terms of the Hermite polynomials. The proof is based on asymptotic combinatorics along with quantum probability theory.

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