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 → +∞, 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.
Propagation of chaos for a balls into bins model
Cancrini N.;
2019-01-01
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 → +∞, 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.File in questo prodotto:
File | Dimensione | Formato | |
---|---|---|---|
CP1.pdf
accesso aperto
Descrizione: Articolo Principale
Tipologia:
Documento in Versione Editoriale
Licenza:
Dominio pubblico
Dimensione
333.61 kB
Formato
Adobe PDF
|
333.61 kB | Adobe PDF | Visualizza/Apri |
Pubblicazioni consigliate
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.