Asymptotic analysis of quadratic error of consensus in large-scale random directed networks

We analyze the asymptotic variance of distributed consensus algorithms over large-scale switching random networks. Our analysis is focused on consensus algorithms over large, i.i.d., and directed Erdős-Rényi random graphs. We assume that every agent can communicate with any other agent with some fixed probability c/n, where c is the expected number of neighbors of each agent and n is the size of the network. We compute the variance of the random consensus value and show that it converges to zero at rate 1/n as the number of agents grows. We provide numerical simulations that illustrate our results.