Matrix Concentration and Equivalent Operators on Fock Spaces
Abstract
We develop a method for proving matrix concentration inequalities by identifying random matrices with associated deterministic operators acting on suitable Fock spaces and controlling norms of these operators and their restrictions to low-order subspaces. Applying this method, we obtain new strengthenings of the non-commutative Khintchine inequality that improve on the state of the art, in particular sharpening recent inequalities due to Bandeira, Boedihardjo, and van Handel (2023) quantifying intrinsic freeness of random matrices. Our proofs of these results are based on relatively simple operator algebra arguments and involve neither Gaussian interpolation nor explicit combinatorics of tracial moments. Further, our techniques apply equally well to several models of non-commutative random variables of interest in the literature, such as operator series constructed from q-Gaussian and Γ-independent systems of operators, treating all of these objects with the same method. We obtain new norm bounds for such operators both in the style of the non-commutative Khintchine inequality and in the style of Lehner's operator norm formula.
Related
- Two-parameter Toeplitz-type operators between Fock spaces
- Positive Toeplitz Operators Between Gaussian Mixed-Norm Fock Spaces
- Absolutely summing Toeplitz operators on weighted Fock spaces
- Comparing positive Toeplitz operators on holomorphic and pluriharmonic Fock spaces
- IDA symbols and Schatten--Lorentz theory for Toeplitz operators on weighted Fock spaces
BibTeX
@misc{bandeira2026matrix,
title = {{Matrix Concentration and Equivalent Operators on Fock Spaces}},
author = {Afonso S. Bandeira and Dmitriy Kunisky and Petar Nizić-Nikolac and Lucas Pesenti and Robert Wang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.01982},
eprint = {2610.01982},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.01982},
}
RIS
TY - UNPB
TI - Matrix Concentration and Equivalent Operators on Fock Spaces
AU - Afonso S. Bandeira
AU - Dmitriy Kunisky
AU - Petar Nizić-Nikolac
AU - Lucas Pesenti
AU - Robert Wang
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.01982
UR - https://arxiv.org/abs/2610.01982
AB - We develop a method for proving matrix concentration inequalities by identifying random matrices with associated deterministic operators acting on suitable Fock spaces and controlling norms of these operators and their restrictions to low-order subspaces. Applying this method, we obtain new strengthenings of the non-commutative Khintchine inequality that improve on the state of the art, in particular sharpening recent inequalities due to Bandeira, Boedihardjo, and van Handel (2023) quantifying intrinsic freeness of random matrices. Our proofs of these results are based on relatively simple operator algebra arguments and involve neither Gaussian interpolation nor explicit combinatorics of tracial moments. Further, our techniques apply equally well to several models of non-commutative random variables of interest in the literature, such as operator series constructed from q-Gaussian and Γ-independent systems of operators, treating all of these objects with the same method. We obtain new norm bounds for such operators both in the style of the non-commutative Khintchine inequality and in the style of Lehner's operator norm formula.
ER -