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Bentley’s conjecture on popularity toplist turnover under random copying
Stockholm University, Faculty of Humanities, Centre for the Study of Cultural Evolution.
Stockholm University, Faculty of Humanities, Centre for the Study of Cultural Evolution.
Stockholm University, Faculty of Humanities, Centre for the Study of Cultural Evolution.
2010 (English)In: The Ramanujan journal, ISSN 1382-4090, E-ISSN 1572-9303, Vol. 23, 371-396 p.Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
2010. Vol. 23, 371-396 p.
Keyword [en]
toplists, random walk, integer partitions, Moran model, popularity distribution
National Category
Mathematics
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:su:diva-51516DOI: 10.1007/s11139-010-9280-zOAI: oai:DiVA.org:su-51516DiVA: diva2:386264
Funder
Swedish Research Council, 1454201
Available from: 2011-01-14 Created: 2011-01-10 Last updated: 2011-01-25Bibliographically approved

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Jansson, Fredrik
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CiteExportLink to record
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Citation style
  • apa
  • ieee
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  • vancouver
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