  This work considers the problem of resilient consensus where stochastic
values of trust between agents are available. Specifically, we derive a unified
mathematical framework to characterize convergence, deviation of the consensus
from the true consensus value, and expected convergence rate, when there exists
additional information of trust between agents. We show that under certain
conditions on the stochastic trust values and consensus protocol: 1) almost
sure convergence to a common limit value is possible even when malicious agents
constitute more than half of the network connectivity, 2) the deviation of the
converged limit, from the case where there is no attack, i.e., the true
consensus value, can be bounded with probability that approaches 1
exponentially, and 3) correct classification of malicious and legitimate agents
can be attained in finite time almost surely. Further, the expected convergence
rate decays exponentially with the quality of the trust observations between
agents.
