Infinite process balls in bins problem Given $n$ balls and $m$ bins, let us consider an infinite process, where in each time slot we throw a ball at a random bin. When all $n$ balls are thrown, we take the balls from the bin with the maximum load, and throw them to random bins.

What the expected number of balls in the bin with the maximum load is converges to?

A variation of the problem is described in https://www.cs.tau.ac.il/~azar/box.pdf, where instead of taken  the bin with the maximum load, a random ball is  selected at random.

In addition, by my experiments, it seems that for $n=\Theta(m)$ the bin with the maximum load converges $2n/m+1$ balls. I am trying to prove  it.
This exact question is answered in this paper: https://arxiv.org/abs/1807.01804