# Traffic distributions and independence: permutation invariant random matrices and the three notions of independence

@article{Male2011TrafficDA, title={Traffic distributions and independence: permutation invariant random matrices and the three notions of independence}, author={Camille Male}, journal={arXiv: Probability}, year={2011} }

Voiculescu's notion of asymptotic free independence is known for a large class of random matrices including independent unitary invariant matrices. This notion is extended for independent random matrices invariant in law by conjugation by permutation matrices. This fact leads naturally to an extension of free probability, formalized under the notions of traffic probability. We first establish this construction for random matrices. We define the traffic distribution of random matrices, which is… CONTINUE READING

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## Large permutation invariant random matrices are asymptotically free over the diagonal

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## FREENESS OVER THE DIAGONAL FOR LARGE RANDOM MATRICES

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## The traffic distribution of the squared unimodular random matrix and a formula for the moments of its ESD

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