### Abstract

In this note, we show that the norm of an n× n random jointly exchangeable matrix with zero diagonal can be estimated in terms of the norm of its ⌊ 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 ⌊ n/ 2 ⌋ × ⌊ n/ 2 ⌋ submatrix. The result has an application to estimating the spectral gap of random undirected d-regular graphs in terms of the second singular value of directed random graphs with predefined degree sequences.

Original language | English (US) |
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Pages (from-to) | 1990-2005 |

Number of pages | 16 |

Journal | Journal of Theoretical Probability |

Volume | 32 |

Issue number | 4 |

DOIs | |

State | Published - Dec 1 2019 |

### Keywords

- Jointly exchangeable
- Random matrix
- Symmetrization

### ASJC Scopus subject areas

- Statistics and Probability
- Mathematics(all)
- Statistics, Probability and Uncertainty

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## Cite this

Tikhomirov, K., & Youssef, P. (2019). On the norm of a random jointly exchangeable matrix.

*Journal of Theoretical Probability*,*32*(4), 1990-2005. https://doi.org/10.1007/s10959-018-0844-y