Universal shocks in the Wishart random-matrix ensemble.

@article{Blaizot2012UniversalSI,
  title={Universal shocks in the Wishart random-matrix ensemble.},
  author={J. P. Blaizot and Maciej A. Nowak and Piotr Warchol},
  journal={Physical review. E, Statistical, nonlinear, and soft matter physics},
  year={2012},
  volume={87 5},
  pages={
          052134
        }
}
We show that the derivative of the logarithm of the average characteristic polynomial of a diffusing Wishart matrix obeys an exact partial differential equation valid for an arbitrary value of N, the size of the matrix. In the large N limit, this equation generalizes the simple inviscid Burgers equation that has been obtained earlier for Hermitian or unitary matrices. The solution, through the method of characteristics, presents singularities that we relate to the precursors of shock formation… 

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