Consider N balls initially placed in L bins. At each time step take a ball from each non-empty bin and randomly reassign all the balls into the bins. We call this finite Markov chain General Repeated Balls into Bins process. It is a discrete time conservative interacting particles system with parallel updates. Assuming a quantitative chaotic condition on the reassignment rule we prove a quantitative propagation of chaos for this model. We furthermore study some equilibrium properties of the limiting nonlinear process.
The present work was financially supported by PRIN 20155PAWZB “Large Scale Random Structures”.
"Propagation of chaos for a general balls into bins dynamics." Electron. J. Probab. 26 1 - 20, 2021. https://doi.org/10.1214/21-EJP590