Electronic Communications in Probability

Propagation of chaos for a balls into bins model

Nicoletta Cancrini and Gustavo Posta

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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.

Article information

Electron. Commun. Probab., Volume 24 (2019), paper no. 1, 9 pp.

Received: 21 September 2018
Accepted: 18 December 2018
First available in Project Euclid: 4 January 2019

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Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 60B10: Convergence of probability measures

chaos propagation interacting particle system parallel updates queues network

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Cancrini, Nicoletta; Posta, Gustavo. Propagation of chaos for a balls into bins model. Electron. Commun. Probab. 24 (2019), paper no. 1, 9 pp. doi:10.1214/18-ECP204. https://projecteuclid.org/euclid.ecp/1546571102

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