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Bentley's conjecture on popularity toplist turnover under random copying
Stockholms universitet.
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
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:kth:diva-90760DOI: 10.1007/s11139-010-9280-zISI: 000284594000025OAI: oai:DiVA.org:kth-90760DiVA: diva2:506463
Note
QC 20120309Available from: 2012-02-28 Created: 2012-02-28 Last updated: 2017-12-07Bibliographically approved

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