Free evolution on algebras with two states, II Academic Article uri icon

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.

published proceedings

  • Pacific Journal of Mathematics

author list (cited authors)

  • Anshelevich, M.

citation count

  • 2

complete list of authors

  • Anshelevich, Michael

publication date

  • July 2015