The stochastic algorithm presented here is by nature embarassingly parallel by dividing the random samples among the available processes while the only communication required is a reduction occurring when each of the independent processes has computed the contribution to the trace associated with its subset of random vectors. Though not being the computational bottleneck, the resolution of the Dyson equations for a set of frequencies is also parallelized with the spatial decomposition strategy embraced within the Tinker-HP package. Similarly to the resolution of the polarisation equations characterizing the AMOEBA force field, each process computes the contribution of the matrix-vector product due to its local p component. At each iteration, in order to compute this matrix vector product, a communication of p at the previous iteration has to be made before the computation and a communication of the result of the product has to be made after. Besides, reductions have to be made to compute the residual (Eq.( )) and the DIIS matrix at each iteration. Because the parallelization scheme is not the same between the iterative solution of the screening equations and the stochastic Lanczos trace estimation, a global broadcast of the screened polarizabilities has to be done between these two steps. Overall, the moderate amount of communication explains the small deviation from the ideal scaling that is observed in Figure after 200 cores.