Random Matrices Theory and Application· 2026Q2
Matrix concentration inequalities for dependent binary random variables
- 1citations
- Q2SCImago
- 2026year
Short summary
New Bernstein-type matrix concentration inequalities are proven for linear combinations of binary random variables with matrix coefficients, under specific independence assumptions.
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Key points
- Proves Bernstein-type matrix concentration inequalities for matrix-valued linear combinations of binary random variables.
- Introduces and utilizes the Stochastic Covering Property and Strong Rayleigh Property for these inequalities.
- Generalizes and strengthens existing estimates for functions satisfying direction-aware matrix bounded difference inequalities.
- Demonstrates a decoupling inequality for Banach-space-valued quadratic forms in negatively associated random variables.
- Extends results on the operator norm of random submatrices to general Strong Rayleigh sampling schemes.
AI-generated from the title and abstract; the full text is not read.
Abstract
We prove Bernstein-type matrix concentration inequalities for linear combinations with matrix coefficients of binary random variables satisfying certain ℓ ∞ -independence assumptions, complementing recent results by Kaufman, Kyng and Solda. For random variables with the Stochastic Covering Property or the Strong Rayleigh Property, we prove estimates for general functions satisfying certain direction-aware matrix bounded difference inequalities, generalizing and strengthening earlier estimates by the first-named author and Polaczyk. We also demonstrate a general decoupling inequality for a class of Banach-space-valued quadratic forms in negatively associated random variables and combine it with the matrix Bernstein inequality to generalize results by Tropp, Chrétien and Darses, and Ruetz and Schnass, concerning the operator norm of a random submatrix of a deterministic matrix, drawn by uniform sampling without replacement or rejective sampling, to submatrices given by general Strong Rayleigh sampling schemes.
The authors' abstract, as published at the source. Random Matrices Theory and Application, 2026 · DOI ↗
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Field: Statistics and Probability
Statistics and ProbabilityMathematics