The smallest singular value of sparse discrete random matrices

Key Points

• The paper establishes a framework for the approximate Spielman-Teng theorem, focusing on sparse discrete random matrices.
• It finds constants where the probability of the smallest singular value being less than η behaves as approximately n^C η plus an exponential decay.
• The analysis extends previous work on random matrices with lazy random variables, contributing to the field of probability theory.
• Results highlight the implications for understanding the behavior of sparse random matrices in various applications.