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We obtain rates of convergence to stationarity in L^1-Wasserstein distancefor a d-dimensional reflected Brownian motion (RBM) in the nonnegative orthantthat are explicit in the dimension and the system parameters. The results arethen applied to a class of RBMs considered in Blanchet-Chen (2016) and torank-based diffusions including the Atlas model. In both cases, we obtainexplicit rates and bounds on relaxation times. In the first case we improve therelaxation time estimates of O(d^4(log d)^2) obtained in Blanchet-Chen (2016)to O((log d)^2). In the latter case, we give the first results on explicitparameter and dimension dependent rates under the Wasserstein distance. Theproofs do not require an explicit form for the stationary measure orreversibility of the process with respect to this measure, and cover settingswhere these properties are not available. In the special case of the standardAtlas model, we obtain a bound on the relaxation time of O(d^6(log d)^2).

Parameter and dimension dependence of convergence rates to stationarity for Reflecting Brownian Motions