Large N expansions for the Laguerre and Jacobi beta-ensembles from the loop equations
Peter J Forrester, Anas A Rahman, Nicholas S Witte
JOURNAL OF MATHEMATICAL PHYSICS | AMER INST PHYSICS | Published : 2017
The β-ensembles of random matrix theory with classical weights have many special properties. One is that the loop equations specifying the resolvent and corresponding multipoint correlators permit a derivation at the general order of the correlator via Aomoto's method from the theory of the Selberg integral. We use Aomoto's method to derive the full hierarchy of loop equations for Laguerre and Jacobi β-ensembles and use these to systematically construct the explicit form of the 1/N expansion at low orders. This allows us to give the explicit form of corrections to the global density and allows various moments to be computed, complementing results available in the literature motivated by prob..View full abstract
Related Projects (2)
Awarded by Australian Research Council
The work of P.J.F. was partially supported by the Australian Research Council Grant No. DP170102028 and the ARC Centre of Excellence for Mathematical and Statistical Frontiers and that of A.A.R. by the Australian Research Council Grant No. DP140102613 and the ARC Centre of Excellence for Mathematical and Statistical Frontiers.