Bentley’s conjecture on popularity toplist turnover under random copying
2010 (English)In: The Ramanujan journal, ISSN 1382-4090, E-ISSN 1572-9303, Vol. 23, 371-396 p.Article in journal (Refereed) Published
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.
toplists, random walk, integer partitions, Moran model, popularity distribution
Research subject Mathematics
IdentifiersURN: urn:nbn:se:su:diva-51516DOI: 10.1007/s11139-010-9280-zOAI: oai:DiVA.org:su-51516DiVA: diva2:386264
FunderSwedish Research Council, 1454201