On the spectral distributions of distance-k graph of free product graphs

2016/01/18 by Octavio Arizmendi, Arizmendi, Octavio, Tulio Gaxiola +1
Mathematics · #Graph theory and applications #Random Matrices and Applications #Advanced Algebra and Geometry

paper · pdf · doi:10.48550/arxiv.1601.04752

Abstract

We calculate the distribution with respect to the vacuum state of the distance-k graph of a d-regular tree. From this result we show that the distance-k graph of a d-regular graphs converges to the distribution of the distance-k graph of a regular tree. Finally, we prove that, properly normalized, the asymptotic distributions of distance-k graphs of the d-fold free product graph, as d tends to infinity, is given by the distribution of P_k(s), where s is a semicircle random variable and P_k is the k-th Chebychev polynomial.

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