Synchronization via Interacting Reinforcement. (June 2014)

• Record Type: Journal Article
• Authors: Dai Pra, Paolo; Louis, Pierre-Yves; Minelli, Ida G.
• Is Part Of: Journal of applied probability. Volume 51:Number 2(2014)
• Page Start: 556
• Page End: 568
• Publication Date: 2014-06
• Subjects: Interacting system, -- synchronization, -- urn model; 60K35, -- 82C31; 519.2
• DOI: 10.1239/jap/1402578643
• Languages: English
• ISSNs: 0021-9002

Abstract

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.