The Traffic Distribution of the Squared Unimodular Random Matrix and a Formula for the Moments of its ESD

The k-th moment of the mean empirical spectral distribution (ESD) of the squared unimodular random matrix of dimension N can be expressed in the form N−2k-1Qk(N), where Qk(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. Puchała, K. Życzkowski [3].