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arXiv · 1709.01498

The traffic distribution of the squared unimodular random matrix and a formula for the moments of its ESD

Jorge Garza Vargas
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Abstract

The $k$-th moment of the mean empirical spectral distribution of the squared unimodular random matrix of dimension $N$ can be expressed in the form $N^{-2k-1} Q_k(N)$, where $Q_k(x)$ is a polynomial of degree $k+1$ with integer coefficients. We use tools from traffic-free probability to express the coefficients of this polynomial in terms of the number of quotients, with a certain property, of some colored directed graphs. The obtained result disproves the formula conjectured in A. Lakshminarayan, Z. Puchala, K. Zyczkowski (2014).

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Jorge Garza Vargas. 2017-09-05. The traffic distribution of the squared unimodular random matrix and a formula for the moments of its ESD. https://arxiv.org/abs/1709.01498

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