A Random Adaptation Perspective on Distributed Averaging

We propose a random adaptation variant of time-varying distributed averaging dynamics in discrete time. show that this leads to novel interpretations fundamental concepts averaging, opinion dynamics, and learning. Namely, we the ergodicity stochastic chain is equivalent almost sure ( xmlns:xlink="http://www.w3.org/1999/xlink">a.s.) finite-time agreement attainment proposed dynamics. Using result, provide new interpretation for xmlns:xlink="http://www.w3.org/1999/xlink">absolute probability sequence an ergodic chain. then modify base-case into time-reversed inhomogeneous Markov chain, case uniqueness limiting distributions Finally, introduce study version Friedkin-Johnsen model rank-one perturbation