Propagation of chaos for a balls into bins model

Electronic Communications in Probability

Nicoletta Cancrini¹ 

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

DOI  :  10.1214/18-ECP204

学科分类：统计和概率

来源: Institute of Mathematical Statistics

【 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 .

【 授权许可】

CC BY