POI count distributions across a city can follow a power law as the weighted sum of locally Poissonian areas with power-law scaled sizes and intensities.
Barthelemy, The Structure and Dynamics of Cities: Urban Data Analysis and Theoretical Modeling (Cam- bridge University Press, Cambridge, 2016)
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Scale-free Points-of-Interest Distribution in a City Emerging from Homogeneous Poissonian-point Processes
POI count distributions across a city can follow a power law as the weighted sum of locally Poissonian areas with power-law scaled sizes and intensities.