In this work we characterize sudden increases in the land price of certain urban areas, a phenomenon causing gentrification, via an extended Schelling model. An initial price rise forces some of the disadvantaged inhabitants out of the area, creating vacancies which other groups find economically attractive. Intolerance issues forces further displacements, possibly giving rise to an avalanche. We consider how gradual changes in the economic environment affect the urban architecture through such avalanche processes, when agents may enter or leave the city freely. The avalanches are characterized by power-law histograms, as it is usually the case in self-organized critical phenomena.
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