We study eigenvalue distribution of the adjacency matrix $A^{ (N,p,q)}$ of weighted random uniform $q$-hypergraphs $\Gamma= \Gamma_{ N,p,q}$. We assume that the graphs have $N$ vertices and the average number of hyperedges attached to one vertex is $(q-1)!\cdot p$. To each edge of the graph $e_{ ij}$ we assign a weight given by a random variable $a_{ ij}$ with all moments finite. We consider the moments of normalized eigenvalue counting function $\sigma_{ N,p,q}$ of $A^{ (N,p,q)}$. Assuming all moments of $a$ finite, we obtain recurrent relations that determine the moments of the limiting measure $\sigma_{ p,q} = \lim_{ N\to\infty} \sigma_{ N,p,q}$.
Categories: math.CO math-ph math.MP