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We analyse the balls in bins process with feedback with primary focus on thepower law feedback function $f(\omega)=\eta \omega^{\gamma}\,$, $\eta>0\,$$\gamma \geq0\,$. Using the recursive solution to the master equation we findfor power law feedback numerical evidence that the probability mass functionfor finite time scales asymptotically with $\omega^{-\gamma}\,$ for$\gamma>1\,$. We also provide simulations supporting a previous result byOliveira (corollary to Theorem 4 in \cite{oliveira2009onset}) that the tail ofthe losers scale as $\omega^{-(\gamma-1)}\,$ but extending to $N \geq 2$ bins.We thus find evidence that the balls in bins process with power law feedbackproduces power law distributions as is common to many real world phenomena.

A Study of the Probability Distribution of the Balls in Bins Process with Power Law Feedback