English

The Spectrum of the Singular Values of Z-Shaped Graph Matrices

Combinatorics 2024-06-26 v2 Discrete Mathematics

Abstract

Graph matrices are a type of matrix which has played a crucial role in analyzing the sum of squares hierarchy on average case problems. However, except for rough norm bounds, little is known about graph matrices. In this paper, we take a step towards better understanding graph matrices by determining the limiting distribution of the spectrum of the singular values of Z-shaped graph matrices. We then give a partial generalization of our results for mm-layer Z-shaped graph matrices.

Keywords

Cite

@article{arxiv.2006.14144,
  title  = {The Spectrum of the Singular Values of Z-Shaped Graph Matrices},
  author = {Wenjun Cai and Aaron Potechin},
  journal= {arXiv preprint arXiv:2006.14144},
  year   = {2024}
}