Operator-valued Jacobi parameters and examples of operator-valued distributions Academic Article uri icon


  • 2017 Elsevier Masson SAS In the setting of distributions taking values in a C -algebra B, we define generalized Jacobi parameters and study distributions they generate. These include numerous known examples and one new family, of B-valued free binomial distributions, for which we are able to compute free convolution powers. Moreover, we develop a convenient combinatorial method for calculating the joint distributions of B-free random variables with Jacobi parameters, utilizing two-color non-crossing partitions. This leads to several new explicit examples of free convolution computations in the operator-valued setting. Additionally, we obtain a counting algorithm for the number of two-color non-crossing pairings of relative finite depth, using only free probabilistic techniques. Finally, we show that the class of distributions with Jacobi parameters is not closed under free convolution.

published proceedings

  • Bulletin des Sciences Mathmatiques

author list (cited authors)

  • Anshelevich, M., & Williams, J. D.

citation count

  • 0

complete list of authors

  • Anshelevich, Michael||Williams, John D

publication date

  • June 2018