Invariant projections for operators that are free over the diagonal
arXiv:1811.03816
Abstract
Motivated by recent work of Au, C{é}bron, Dahlqvist, Gabriel, and Male, we study regularity properties of the distribution of a sum of two selfad-joint random variables in a tracial noncommutative probability space which are free over a commutative algebra. We give a characterization of the invariant projections of such a sum in terms of the associated subordination functions.
Preliminary version, 13 pages, LaTeX. Comments are most welcome
References in corpus (4)
- Freely Independent Random Variables with Non-Atomic Distributions
- Large permutation invariant random matrices are asymptotically free over the diagonal
- The free field: zero divisors, Atiyah property and realizations via unbounded operators
- Hölder Continuity of Cumulative Distribution Functions for Noncommutative Polynomials under Finite Free Fisher Information