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Bentley’s conjecture on popularity toplist turnover under random copying
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- Eriksson, Kimmo (author)
- Mälardalens högskola,Stockholms universitet,Centrum för evolutionär kulturforskning,Akademin för utbildning, kultur och kommunikation,CEK
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- Jansson, Fredrik (author)
- Mälardalens högskola,Stockholms universitet,Centrum för evolutionär kulturforskning,Akademin för utbildning, kultur och kommunikation,CEK
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- Sjöstrand, Jonas (author)
- Stockholms universitet,Centrum för evolutionär kulturforskning,KTH
- (creator_code:org_t)
- 2010-10-28
- 2010
- English.
- In: The Ramanujan journal. - : Springer Science and Business Media LLC. - 1382-4090 .- 1572-9303. ; 23, s. 371-396
- Journal article (peer-reviewed)
Abstract
Subject headings
Close
- Bentley et al studied the turnover rate in popularity toplists in a ’random copying’ model of cultural evolution. Based on simulations of a model with population size N, list length ℓ and invention rate μ, they conjectured a remarkably simple formula for the turnover rate: ℓ√μ. Here we study an overlapping generations version of the random copying model, which can be interpreted as a random walk on the integer partitions of the population size. In this model we show that the conjectured formula, after a slight correction, holds asymptotically.
Subject headings
- NATURVETENSKAP -- Matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics (hsv//eng)
- NATURVETENSKAP -- Matematik -- Sannolikhetsteori och statistik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Probability Theory and Statistics (hsv//eng)
Keyword
- toplists
- random walk
- integer partitions
- Moran model
- popularity distribution
- MATHEMATICS
- MATEMATIK
- Mathematics
- matematik
- Mathematics/Applied Mathematics
Publication and Content Type
- ref (subject category)
- art (subject category)
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- Jansson, Fredrik
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