Agnostic conservative down-sampling for optimizing statistical representations and PIC simulations

In particle-in-cell simulations and some other statistical computations, the representation of modelled distributions with tracked macro-particles can become locally excessive. Merging or resampling dense clusters or highly-populated phase space volumes may, however, remove or affect small-scale peculiarities in the modelled distribution or cause local changes of conserved quantities, such as energy and momenta. This may lead to additional noise, reduced accuracy or even unphysical effects. Here we describe a probabilistic algorithm for reducing the number of macro-particles in such clusters or volumes so that all the distribution functions are not affected on average and an arbitrary number of conservation laws, distribution central moments and contributions to the grid quantities (such as charge and current density) are preserved.