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Bentley’s conjecture on popularity toplist turnover under random copying

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Abstract

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: \(\ell \sqrt{\mu}\). 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.

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Authors and Affiliations

  1. School of Communication, Culture and Communication, Mälardalen University, 721 23, Västerås, Sweden

    Kimmo Eriksson, Fredrik Jansson & Jonas Sjöstrand

  2. Centre for the Study of Cultural Evolution at Stockholm University, Stockholm, Sweden

    Kimmo Eriksson, Fredrik Jansson & Jonas Sjöstrand

Authors
  1. Kimmo Eriksson
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  2. Fredrik Jansson
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  3. Jonas Sjöstrand
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Corresponding author

Correspondence to Kimmo Eriksson.

Additional information

Dedicated to George Andrews for his 70th birthday

This research was supported by the CULTAPTATION project (European Commission contract FP6-2004-NEST-PATH-043434) and the Swedish Research Council.

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Eriksson, K., Jansson, F. & Sjöstrand, J. Bentley’s conjecture on popularity toplist turnover under random copying. Ramanujan J 23, 371–396 (2010). https://doi.org/10.1007/s11139-010-9280-z

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  • DOI: https://doi.org/10.1007/s11139-010-9280-z

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