Wednesday, June 19, 2013

1306.4014 (Jean-Paul Blaizot et al.)

Universal shocks in the Wishart random-matrix ensemble - a sequel    [PDF]

Jean-Paul Blaizot, Maciej A. Nowak, Piotr Warchoł
We study the diffusion of complex Wishart matrices and derive a partial differential equation governing the behavior of the associated averaged characteristic polynomial. In the limit of large size matrices, the inverse Cole-Hopf transform of this polynomial obeys a nonlinear partial differential equation whose solutions exhibit shocks at the evolving edges of the eigenvalue spectrum. In a particular scenario one of those shocks hits the origin that plays the role of an impassable wall. To study the universal behavior in the vicinity of this wall, a critical point, we derive an integral representation for the averaged characteristic polynomial and study its asymptotic behavior. The result is a modification of a so-called Bessoid function.
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