Journal of Applied Probability

Synchronization via interacting reinforcement

Paolo Dai Pra, Pierre-Yves Louis, and Ida G. Minelli

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Abstract

We consider a system of urns of Pólya type, containing balls of two colors; the reinforcement of each urn depends on both the content of the urn and the average content of all urns. We show that the urns synchronize almost surely, in the sense that the fraction of balls of a given color converges almost surely as time tends to ∞ to the same limit for all urns. A normal approximation for a large number of urns is also obtained.

Article information

Source
J. Appl. Probab., Volume 51, Number 2 (2014), 556-568.

Dates
First available in Project Euclid: 12 June 2014

Permanent link to this document
https://projecteuclid.org/euclid.jap/1402578643

Digital Object Identifier
doi:10.1239/jap/1402578643

Mathematical Reviews number (MathSciNet)
MR3217785

Zentralblatt MATH identifier
1305.60105

Subjects
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 82C31: Stochastic methods (Fokker-Planck, Langevin, etc.) [See also 60H10]

Keywords
Interacting system synchronization urn model

Citation

Dai Pra, Paolo; Louis, Pierre-Yves; Minelli, Ida G. Synchronization via interacting reinforcement. J. Appl. Probab. 51 (2014), no. 2, 556--568. doi:10.1239/jap/1402578643. https://projecteuclid.org/euclid.jap/1402578643


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