Propagation of chaos for a balls into bins model

[摘要] Consider a finite number of balls initially placed in $L$ bins. At each time step a ball is taken from each non-empty bin. Then all the balls are uniformly reassigned into bins. This finite Markov chain is called Repeated Balls-into-Bins process and is a discrete time interacting particle system with parallel updating. We prove that, starting from a suitable ( chaotic ) set of initial states, as $L\to +\infty $, the numbers of balls in each bin become independent from the rest of the system i.e. we have propagation of chaos . We furthermore study some equilibrium properties of the limiting nonlinear process .

[学科分类] 统计和概率

[关键词] chaos propagation;interacting particle system;parallel updates;queues network