# On the norm of a random jointly exchangeable matrix

@article{Tikhomirov2018OnTN,
title={On the norm of a random jointly exchangeable matrix},
author={Konstantin E. Tikhomirov and Pierre Youssef},
journal={Journal of Theoretical Probability},
year={2018},
pages={1-16}
}
• Published 6 October 2016
• Mathematics
• Journal of Theoretical Probability
In this note, we show that the norm of an $$n\times n$$n×n random jointly exchangeable matrix with zero diagonal can be estimated in terms of the norm of its $$\lfloor n/2\rfloor \times \lfloor n/2\rfloor$$⌊n/2⌋×⌊n/2⌋ submatrix located in the top right corner. As a consequence, we prove a relation between the second largest singular values of a random matrix with constant row and column sums and its top right $$\lfloor n/2\rfloor \times \lfloor n/2\rfloor$$⌊n/2⌋×⌊n/2⌋ submatrix. The result… Expand
1 Citations
The spectral gap of dense random regular graphs
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For any $\alpha\in (0,1)$ and any $n^{\alpha}\leq d\leq n/2$, we show that $\lambda(G)\leq C_\alpha \sqrt{d}$ with probability at least $1-\frac{1}{n}$, where $G$ is the uniform random $d$-regularExpand

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