Arpan Mukhopadhyay: Computation of Absorption Times of Markov Processes Corresponding to Models of Opinion Dynamics

In this talk, I shall focus on two simple models of opinion propagation in a network of interacting agents, namely, i) the voter model and ii) the majority rule model. These models describe how opinions propagate as a result of random interactions among agents in the network. For fully connected networks, it is known that with probability one in a finite time the network gets absorbed in a consensus state, where all the agents adopt the same opinion. In many cases, it is of interest to determine how the consensus time (time of absorption) scales as a function of the network size. In this talk, I shall focus on the different techniques for computation of absorption time. In particular, I shall show that the absorption time for large networks can be well approximated by a deterministic time which is the first time a fluid approximation of the corresponding network approaches the absorbing state at a negligible distance. This method is particularly useful when a direct computation of the absorption time becomes difficult.