Non asymptotic bounds in asynchronous sum-weight gossip protocols

This paper focuses on non-asymptotic diffusion time in asynchronous gossip protocols. Asynchronous gossip protocols are designed to perform distributed computation in a network of nodes by randomly exchanging messages on the associated graph. To achieve consensus among nodes, a minimal number of messages has to be exchanged. We provides a probabilistic bound to such number for the general case. We provide a explicit formula for fully connected graphs depending only on the number of nodes and an approximation for any graph depending on the spectrum of the graph.