Electronic Communications in Probability
- Electron. Commun. Probab.
- Volume 24 (2019), paper no. 1, 9 pp.
Propagation of chaos for a balls into bins model
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.
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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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