On convergence rate to synchronization in stochastic particle systems

We study a multidimensional Markov process describing a symmetric system of N identical Brownian particles with pair synchronizing interaction. In moving coordinate systems, related to one of the particles, we provide close upper and lower bounds of the convergence rate to a limiting distribution in the total variation metric. In order to prove the bounds some auxiliary processes are introduced. The idea of their construction resembles the coupling method.