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Propagation of chaos for a balls into bins model. (English) Zbl 1406.60128
Summary: 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 \(L\rightarrow +\infty \), 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.

MSC:
60K35 Interacting random processes; statistical mechanics type models; percolation theory
60B10 Convergence of probability measures
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