On the norm of a random jointly exchangeable matrix

Konstantin Tikhomirov () and Pierre Youssef ()
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Konstantin Tikhomirov: Princeton University
Pierre Youssef: Université Paris Diderot

Journal of Theoretical Probability, 2019, vol. 32, issue 4, 1990-2005

Abstract: Abstract 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 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.

Keywords: Random matrix; Jointly exchangeable; Symmetrization; 60B20; 15B52 (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s10959-018-0844-y

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