Byzantine fault-tolerant consensus over random graph processes

In this work, we consider the problem of distributed consensus when some agents in the network are faulty and communication among agents happen over a random sequence of time-varying graphs. Agents iteratively communicate with their neighbors to achieve the consensus. We extend the network robustness condition presented in existing works on static (or time-varying but not random) graphs to the situation when communication graphs are derived from some probability distribution thus essentially random. We show that if the sequence of random graphs is uniformly stochastically robust, then the consensus can be achieved almost surely by all non-faulty agents.