FREE EVOLUTION ON ALGEBRAS WITH TWO STATES, II
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abstract
Denote by J the operator of coefficient stripping. We show that for any free convolution semigroup {t: t 0} with finite variance, applying a single stripping produces semicircular evolution with nonzero initial condition, J [t] = {squared plus} {squared plus}t; , , where , is the semicircular distribution with mean and variance . For more general freely infinitely divisible distributions , expressions of the form {squared plus}{squared plus}t arise from stripping t , where {t;t 0} 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.