Strongly reinforced Pólya urns with graph-based competition

R.W. Hofstad, van der, M.P. Holmes, A. Kuznetsov, W.M. Ruszel

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We introduce a class of reinforcement models where, at each time step t, one ¿rst chooses a random subset A_t of colours (independent of the past) from n colours of balls, and then chooses a colour i from this subset with probability proportional to the number of balls of colour i in the urn raised to the power a > 1. We consider stability of equilibria for such models and establish the existence of phase transitions in a number of examples, including when the colours are the edges of a graph, a context which is a toy model for the formation and reinforcement of neural connections. Keywords: reinforcement model, Pólya urn, stochastic approximation algorithm, stable equilibria
Original languageEnglish
Place of PublicationEindhoven
Number of pages32
Publication statusPublished - 2014

Publication series

NameReport Eurandom
ISSN (Print)1389-2355


Cite this

Hofstad, van der, R. W., Holmes, M. P., Kuznetsov, A., & Ruszel, W. M. (2014). Strongly reinforced Pólya urns with graph-based competition. (Report Eurandom; Vol. 2014015). Eindhoven: Eurandom.