# Propagation of chaos for a General Balls into Bins dynamics

## TL;DR

This paper proves a quantitative propagation of chaos for a Markov chain model where balls are redistributed among bins, and explores equilibrium properties of the limiting nonlinear process.

## Contribution

It introduces a new analysis of the General Repeated Balls into Bins process, establishing quantitative propagation of chaos under specific conditions.

## Key findings

- Quantitative propagation of chaos established
- Analysis of equilibrium properties of the nonlinear limit
- Model provides insights into interacting particle systems

## Abstract

Consider $N$ balls initially placed in $L$ bins. At each time step take a ball from each non-empty bin and \emph{randomly} reassign the balls into the bins.We call this finite Markov chain \emph{General Repeated Balls into Bins} process. It is a discrete time interacting particles system with parallel updates. Assuming a \emph{quantitative} chaotic condition on the reassignment rule we prove a \emph{quantitative} propagation of chaos for this model. We furthermore study some equilibrium properties of the limiting nonlinear process.