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arXiv · 1406.0449

Strongly reinforced P\'olya urns with graph-based competition

Remco van der Hofstad·Mark Holmes·Alexey Kuznetsov·Wioletta Ruszel
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Abstract

We introduce a class of reinforcement models where, at each time step $t$, one first 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 $\alpha>1$. 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.

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Remco van der Hofstad, Mark Holmes, Alexey Kuznetsov, Wioletta Ruszel. 2014-06-02. Strongly reinforced P\'olya urns with graph-based competition. https://arxiv.org/abs/1406.0449

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