# Random Laplacian Matrices and Convex Relaxations

@article{Bandeira2018RandomLM,
title={Random Laplacian Matrices and Convex Relaxations},
author={A. Bandeira},
journal={Foundations of Computational Mathematics},
year={2018},
volume={18},
pages={345-379}
}
• A. Bandeira
• Published 2018
• Mathematics, Computer Science
• Foundations of Computational Mathematics
• The largest eigenvalue of a matrix is always larger or equal than its largest diagonal entry. We show that for a class of random Laplacian matrices with independent off-diagonal entries, this bound is essentially tight: the largest eigenvalue is, up to lower order terms, often the size of the largest diagonal. entry. Besides being a simple tool to obtain precise estimates on the largest eigenvalue of a class of random Laplacian matrices, our main result settles a number of open problems related… CONTINUE READING
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