On the norm of a random jointly exchangeable matrix

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.