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We investigate the randomized Karlin model with parameter $\beta\in(0,1)$,which is based on an infinite urn scheme. It has been shown before that whenthe randomization is bounded, the so-called odd-occupancy process scales to afractional Brownian motion with Hurst index $\beta/2\in(0,1/2)$. We show herethat when the randomization is heavy-tailed with index $\alpha\in(0,2)$, thenthe odd-occupancy process scales to a $(\beta/\alpha)$-self-similar symmetric$\alpha$-stable process with stationary increments.

From infinite urn schemes to self-similar stable processes