Particle systems with mean-field interaction arise as models in a variety of applications: peer-to-peer synchronization; parallel simulation; blockchains; evolution of prices; workload dynamics in parallel queues; etc. In such systems, each particle make random jumps at the rate depending on its location and the empirical distribution of all particles' locations. For a large-scale system -- with the number n of particles increasing to infinity -- some of the questions of interest are: Does the system dynamics converge to that of a mean-field model (MFM)? Do MFMs that are traveling waves exist/unique? Do MFMs converge to traveling waves (as time increases)? Does the stationary distribution concentrate on a traveling wave (as n increases)? This talk addresses some of these questions, with the primary focus on the rank-based interaction model.
