Convergence Rate of Empirical Spectral Distribution of Random Matrices from Linear Codes

Abstract

It is known that the empirical spectral distribution of random matrices obtained from linear codes of increasing length converges to the well-known Marchenko-Pastur law, if the Hamming distance of the dual codes is at least 5. In this paper, we prove that the convergence in probability is at least of the order $n^{-1/4}$ where $n$ is the length of the code.

References in corpus (5)

• Construction of a Large Class of Deterministic Sensing Matrices that Satisfy a Statistical Isometry Property
• Universality of covariance matrices
• Universality of Wigner random matrices: a Survey of Recent Results
• Exponential Weighting and Random-Matrix-Theory-Based Filtering of Financial Covariance Matrices for Portfolio Optimization
• Restricted isometry property of random subdictionaries

Cited by in corpus (1)

• Random Matrices from Linear Codes and Wigner's Semicircle Law II