Convergence rate of the diagonal-valued Cauchy-transform for permutation invariant random matrices
Abstract
Let $A$ be a permutation invariant random matrix and $B$ another random matrix. We give a quantitative bound on the difference between the diagonal of the resolvent of $A+B$ and the diagonal of the resolvent of the free sum with amalgamation over the diagonal of $A$ and $B$. Moreover, we improve the rate of convergence whenever the matrices $A$ and $B$ are sparse and bounded in operator norm. Doing so, we explicitly construct the free sum over the diagonal of $A$ and $B$ as an adjacency operator of a weighted locally finite graph.
Fields of Study & Subjects
Random Matrices and Applications
Spectral Theory in Mathematical Physics
Advanced Operator Algebra Research
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 2 March 2026
- Language
- EN
- Document type
- Preprint