%0 Journal Article
%T Strongly reinforced P¨Žlya urns with graph-based competition
%A Remco van der Hofstad
%A Mark Holmes
%A Alexey Kuznetsov
%A Wioletta Ruszel
%J Mathematics
%D 2014
%I arXiv
%X 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.
%U http://arxiv.org/abs/1406.0449v1