Nonlinear random matrix statistics, symmetric functions and hyperdeterminants
Abstract
Nonlinear statistics (i.e. statistics of permanents) on the eigenvalues of invariant random matrix models are considered for the three Dyson's symmetry classes β = 1, 2, 4. General formulas in terms of hyperdeterminants are found for β = 2. For specific cases and all βs, more computationally efficient results are obtained, based on symmetric functions expansions. As an application, we consider the case of quantum transport in chaotic cavities extending results from Savin et al (2008 Phys. Rev. B 77 125332).
 Publication:

Journal of Physics A Mathematical General
 Pub Date:
 February 2010
 DOI:
 10.1088/17518113/43/8/085213
 arXiv:
 arXiv:0912.1228
 Bibcode:
 2010JPhA...43h5213L
 Keywords:

 Mathematical Physics;
 Condensed Matter  Statistical Mechanics
 EPrint:
 16 pages, 4 figures