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We study random band matrices within the framework of traffic probability, an operadic non-commutative probability theory introduced by Male based on graph operations.
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Benson Au and Camille Male, Canonical structures in traffic spaces: with a view toward random matrices , in preparation
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James A. Mingo and Roland Speicher, Sharp bounds for sums associated to graphs of matrices , J. Funct. Anal. 262
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László Erdős and Horng-Tzer Yau, Dynamical approach to random matrix theory , in preparation. Preliminary version available at http://www.math.harvard.edu/ htyau/Random-Matrix-Aug-2016.pdf
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Xue Ding and Tiefeng Jiang, Spectral distributions of adjacency and Laplacian matrices of random graphs , Ann. Appl. Probab. 20
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