Papers › A Study of the Probability Distribution of the Balls in Bins Process with Power Law Feedback
A Study of the Probability Distribution of the Balls in Bins Process with Power Law Feedback
Samuel Forbes
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We analyse the balls in bins process with feedback with primary focus on the power law feedback function f(ω)=ηω^γ, η>0 γ≥0. Using the recursive solution to the master equation we find for power law feedback numerical evidence that the probability mass function for finite time scales asymptotically with ω^(-γ) for γ>1. We also provide simulations supporting a previous result by Oliveira (corollary to Theorem 4 in \cite{oliveira2009onset}) that the tail of the losers scale as ω^(-(γ-1)) but extending to N ≥2 bins. We thus find evidence that the balls in bins process with power law feedback produces power law distributions as is common to many real world phenomena.
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