On the norm of a random jointly exchangeable matrix

Konstantin Tikhomirov, Pierre Youssef

Research output: Contribution to journalArticle

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 languageEnglish (US)
Pages (from-to)1990-2005
Number of pages16
JournalJournal of Theoretical Probability
Volume32
Issue number4
DOIs
StatePublished - 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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