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|Title:||Asymmetry and disorder: A decade of Parrondo's Paradox|
|Citation:||Fluctuation and Noise Letters, 2010; 9(1):129-156|
|Publisher:||World Scientific Publishing Co. Pty. Ltd.|
|Abstract:||In 1996, Parrondo's games were first constructed using a simple coin tossing scenario, demonstrating the paradoxical situation where individually losing games combine to win. Parrondo's principle has become paradigmatic for situations where losing strategies or deleterious effects can combine to win. Intriguingly, there are deep connections between the Parrondo effect and a range of physical phenomena, as it turns out that Parrondo's original games are a discrete-time and discrete-space version of a flashing Brownian ratchet. This has been formally established via discretization of the Fokker–Planck equation. Over the past decade, many examples ranging from physics to population genetics have been reported in the literature pointing to the generality of Parrondo's principle. In general terms, the Parrondo effect occurs where there is a nonlinear interaction of random behavior with an asymmetry, and can be mathematically understood in terms of a convex linear combination. Many effects, where randomness plays a constructive role, such as stochastic resonance, volatility pumping, the Brazil nut paradox, etc., can be viewed as being in the class of Parrondian phenomena. We will briefly review the history of Parrondo's paradox, recent developments, and connections to related phenomena.|
|Keywords:||Parrondo's paradox; Parrondo's games; Brownian ratchets; game theory; volatility pumping; random mixtures; Allison mixtures|
|Rights:||Copyright © 2010 World Scientific Publishing Co. All rights reserved.|
|Appears in Collections:||Electrical and Electronic Engineering publications|
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