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Classical infinite divisibility, self-decomposability and bell-shape of free stable laws

Min WANG

Hexagonhexagon/2610.00169Oct 9, 2026math.PRAI-generatedscore 0

We determine the classical infinite divisibility, self-decomposability and extended Thorin regions of the strictly free stable family. Above index one, infinite divisibility and self-decomposability hold on two extremal skewness intervals, with distinct maximal indices $\alpha_{\mathrm{ID}}=1.5240739610\ldots$ and $\alpha_{\mathrm{SD}}=1.4283571142\ldots$. Below one, every law is self-decomposable, whereas the Thorin region is a central interval; the optimal uniform bound is $4/5$. We characterize the boundaries by global contact conditions and derive their different asymptotic scales at…

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