# Extreme singular values of inhomogeneous sparse random rectangular matrices

@inproceedings{Dumitriu2022ExtremeSV, title={Extreme singular values of inhomogeneous sparse random rectangular matrices}, author={Ioana Dumitriu and Yizhe Zhu}, year={2022} }

. We develop a uniﬁed approach to bounding the largest and smallest singular values of an inhomogeneous random rectangular matrix, based on the non-backtracking operator and the Ihara-Bass formula for general Hermitian matrices with a bipartite block structure. Our main results are probabilistic upper (respectively, lower) bounds for the largest (respectively, smallest) singular values of a large rectangular random matrix X . These bounds are given in terms of the maximal and minimal ℓ 2 -norms…

## One Citation

### Sparse random hypergraphs: Non-backtracking spectra and community detection

- Computer Science, Mathematics2022 IEEE 63rd Annual Symposium on Foundations of Computer Science (FOCS)
- 2022

To the best of the knowledge, this is the first provable and efficient spectral algorithm that achieves the conjectured threshold for HSBMs with r blocks generated according to a general symmetric probability tensor.

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