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2019 Propagation of chaos for a balls into bins model
Nicoletta Cancrini, Gustavo Posta
Electron. Commun. Probab. 24(none): 1-9 (2019). DOI: 10.1214/18-ECP204

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.

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Nicoletta Cancrini. Gustavo Posta. "Propagation of chaos for a balls into bins model." Electron. Commun. Probab. 24 1 - 9, 2019. https://doi.org/10.1214/18-ECP204

Information

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

zbMATH: 1406.60128
MathSciNet: MR3908646
Digital Object Identifier: 10.1214/18-ECP204

Subjects:
Primary: 60B10, 60K35

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