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- Title
The Orthogonal Polynomials for a Linear Sum of a Free Family of Projections.
- Authors
Akiyama, Mai; Yoshida, Hiroaki
- Abstract
We calculate the probability measures for some linear combinations of a free family of projections by using Voiculescu's R-transform for free additive convolution in the free probability theory. The measures we give in this paper include many examples that have been calculated, for instance, the spectral measure for the adjacency operators of the infinite distance regular graphs, and the Plancherel measures associated with free product groups. Furthermore, we find the recursive relations for the orthogonal polynomials associated with them.
- Subjects
FREE probability theory; PROBABILITY measures; LINEAR systems
- Publication
Infinite Dimensional Analysis, Quantum Probability & Related Topics, 1999, Vol 2, Issue 4, p627
- ISSN
0219-0257
- Publication type
Article
- DOI
10.1142/S0219025799000357