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Zipf's, Heaps' and Taylor's laws are determined by the expansion into the adjacent possible
Zipf's, Heaps' and Taylor's laws are ubiquitous in many different systems
where innovation processes are at play. Together, they represent a compelling
set of stylized facts regarding the overall statistics, the innovation rate and
the scaling of fluctuations for systems as diverse as written texts and cities,
ecological systems and stock markets. Many modeling schemes have been proposed
in literature to explain those laws, but only recently a modeling framework has
been introduced that accounts for the emergence of those laws without deducing
the emergence of one of the laws from the others or without ad hoc assumptions.
This modeling framework is based on the concept of adjacent possible space and
its key feature of being dynamically restructured while its boundaries get
explored, i.e., conditional to the occurrence of novel events. Here, we
illustrate this approach and show how this simple modelling framework,
instantiated through a modified Polya's urn model, is able reproduce Zipf's,
Heaps' and Taylor's laws within a unique self-consistent scheme. In addition
the same modelling scheme embraces other less common evolutionary laws (Hoppe's
model and Dirichlet processes) as particular cases.Comment: This article belongs to the Special Issue Economic Fitness and
Complexit