Strong convergence to operator-valued semicirculars
Fuente:
arXiv
Guardado en:
| Autores principales: | , , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866914060269780992 |
|---|---|
| author | Jekel, David Lee, Yoonkyeong Nelson, Brent Pi, Jennifer |
| author_facet | Jekel, David Lee, Yoonkyeong Nelson, Brent Pi, Jennifer |
| contents | We establish a framework for weak and strong convergence of matrix models to operator-valued semicircular systems parametrized by operator-valued covariance matrices $η= (η_{i,j})_{i,j \in I}$. Non-commutative polynomials are replaced by covariance polynomials that can involve iterated applications of $η_{i,j}$, leading to the notion of covariance laws. We give sufficient conditions for weak and strong convergence of general Gaussian random matrices and deterministic matrices to a $B$-valued semicircular family and generators of the base algebra $B$. In particular, we obtain operator-valued strong convergence for continuously weighted Gaussian Wigner matrices, such as Gaussian band matrices with a continuous cutoff, and we construct natural strongly convergent matrix models for interpolated free group factors. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_19940 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Strong convergence to operator-valued semicirculars Jekel, David Lee, Yoonkyeong Nelson, Brent Pi, Jennifer Operator Algebras Probability We establish a framework for weak and strong convergence of matrix models to operator-valued semicircular systems parametrized by operator-valued covariance matrices $η= (η_{i,j})_{i,j \in I}$. Non-commutative polynomials are replaced by covariance polynomials that can involve iterated applications of $η_{i,j}$, leading to the notion of covariance laws. We give sufficient conditions for weak and strong convergence of general Gaussian random matrices and deterministic matrices to a $B$-valued semicircular family and generators of the base algebra $B$. In particular, we obtain operator-valued strong convergence for continuously weighted Gaussian Wigner matrices, such as Gaussian band matrices with a continuous cutoff, and we construct natural strongly convergent matrix models for interpolated free group factors. |
| title | Strong convergence to operator-valued semicirculars |
| topic | Operator Algebras Probability |
| url | https://arxiv.org/abs/2506.19940 |