There are $n$ stones distributed in $n$ buckets (initially one stone in each bucket). At each step the content of each bucket is put in a random bucket, chosen independently out of a set of $n$ new empty buckets. Doing this the groups of stones in the differents buckets may merge together.

Now, after $i$ steps we consider the non-empty groups of stones, and I was wondering if there is any information about the (two dimensional) distribution (giving a probability of having at least $\geq b$ buckets with $\geq k$ stones, say), in particular if the problem was studied for big $n$ and big $i$ relative to $n$. Was this model studied before?

The problem arises from simulations of discretized chaotic dynamical systems, where this model (could) provide a comparison model, for long time behaviour and fine discretization.

andup joining and formingsgroups, that at each stepmymerge in a smaller number of bigger groups." This sentence has so many typos that I had trouble following. I have an idea what you want to say (add/forming/they), but would you mind correcting it? Also some other things (ofter, ...). $\endgroup$ – bers Jun 16 '16 at 14:25