## Electronic Communications in Probability

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

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

Nicoletta Cancrini and Gustavo Posta

#### 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**

Received: 21 September 2018

Accepted: 18 December 2018

First available in Project Euclid: 4 January 2019

**Permanent link to this document**

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

**Digital Object Identifier**

doi:10.1214/18-ECP204

**Mathematical Reviews number (MathSciNet)**

MR3908646

**Zentralblatt MATH identifier**

1406.60128

**Subjects**

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

**Keywords**

chaos propagation interacting particle system parallel updates queues network

**Rights**

Creative Commons Attribution 4.0 International License.

#### 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