Figure 4.

Heaps’ law (left) and Zipf’s law (right) in the urn model with triggering. Straight lines in the Heaps’ law plots show functions of the form $f\left(x\right)=a{x}^{\gamma }$ with the exponent $\gamma =\nu /\rho$ as predicted by the analytic results and confirmed in the numerical simulations. Straight lines in the Zipf’s law plots show functions of the form $f\left(x\right)=a{x}^{-\alpha }$, with $\alpha ={\gamma }^{-1}=\rho /\nu$.