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Abstract

Denote by J the operator of coefficient stripping. We show that for any free convolution semigroup f t W t 0g with finite variance, applying a single stripping produces semicircular evolution with nonzero initial condition, J OE t D ť ; , where ˇ; is the semicircular distribution with meanˇand variance . For more general freely infinitely divisible distributions , expressions of the form Q t arise from stripping Q t , where f. Q t ; t / W t 0g forms a semigroup under the operation of two-state free convolution. The converse to this statement holds in the algebraic setting. Numerous examples illustrating these constructions are computed. Additional results include the formula for generators of such semigroups.