## Electronic Communications in Probability

### Propagation of chaos for a balls into bins model

#### Abstract

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

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

Dates
Accepted: 18 December 2018
First available in Project Euclid: 4 January 2019

https://projecteuclid.org/euclid.ecp/1546571102

Digital Object Identifier
doi:10.1214/18-ECP204

#### Citation

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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