Discrete--time ratchets, the Fokker--Planck equation and Parrondo's paradox
Parrondo's games manifest the apparent paradox where losing strategies can be combined to win and have generated significant multidisciplinary interest in the literature. Here we review two recent approaches, based on the Fokker-Planck equation, that rigorously establish the connection between...
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Main Authors | , , , |
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Format | Journal Article |
Language | English |
Published |
28.08.2003
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Subjects | |
Online Access | Get full text |
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Summary: | Parrondo's games manifest the apparent paradox where losing strategies can be
combined to win and have generated significant multidisciplinary interest in
the literature. Here we review two recent approaches, based on the
Fokker-Planck equation, that rigorously establish the connection between
Parrondo's games and a physical model known as the flashing Brownian ratchet.
This gives rise to a new set of Parrondo's games, of which the original games
are a special case. For the first time, we perform a complete analysis of the
new games via a discrete-time Markov chain (DTMC) analysis, producing winning
rate equations and an exploration of the parameter space where the paradoxical
behaviour occurs. |
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DOI: | 10.48550/arxiv.cond-mat/0308609 |