This survey covers models of how agents update behaviors and beliefs using information
conveyed through social connections. We begin with sequential social learning models, in …

Recent progress on the understanding of the Random Conductance Model is reviewed and
commented. A particular emphasis is on the results on the scaling limit of the random walk …

We prove an optimal mixing time bound for the single-site update Markov chain known as
the Glauber dynamics or Gibbs sampling in a variety of settings. Our work presents an …

We study learning in a setting where agents receive independent noisy signals about the
true value of a variable and then communicate in a network. They naïvely update beliefs by …

We examine how the speed of learning and best-response processes depends on
homophily: the tendency of agents to associate disproportionately with those having similar …

The use of simulation for high-dimensional intractable computations has revolutionized
applied mathematics. Designing, improving and understanding the new tools leads to (and …

This paper studies the algorithmic stability and generalizability of decentralized stochastic
gradient descent (D-SGD). We prove that the consensus model learned by D-SGD is …

Unlike the Telephone network or the Internet, many of the next generation networks are not
engineered for the purpose of providing efficient communication between various networked …

Given a universal gate set on two qubits, it is well known that applying random gates from
the set to random pairs of qubits will eventually yield an approximately Haar-distributed …

This paper discusses practical consensus-based distributed optimization algorithms. In
consensus-based optimization algorithms, nodes interleave local gradient descent steps …