Stochastic compression with and without permutations

We consider a simplified mass redistribution scheme, with and without permutations, that simulates stochastic compression under high and low disorder. For this case, surprisingly, the limit density distributions can be computed explicitly, and neat formulas are provided. As the dimension of space increases, the distinction between structured and turbulent compression becomes less pronounced. Already in dimension two, the density distributions are barely distinguishable. • Analytical results for limit densities in a stochastic compression process. • Comparison of asymptotic behavior with and without permutations. • Extension of some results to the multidimensional case.