Convergence rate in stochastic particle systems with synchronization

A multidimensional Markov process $x(t) = (x_1(t),\ldots, x_N(t))$, $t \in \mathbf{R}_+$, describing a system of $N$ identical Brownian particles with synchronizing interaction is considered. In relative coordinates, connected with the moving observer, similar upper and lower bounds of the rate of convergence to the limit distribution of the distance metric for variation are obtained.