On the norm of a random jointly exchangeable matrix

18 Nov 2016  ·  Tikhomirov Konstantin, Youssef Pierre ·

In this note, we show that the norm of an $n\times n$ random jointly exchangeable matrix with zero diagonal can be estimated in terms of the norm of its $n/2\times n/2$ 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 $n/2\times n/2$ 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 {\it directed} random graphs with predefined degree sequences. read more

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Probability Combinatorics