Spectral statistics of the uni-modular ensemble
Spectral statistics of the uni-modular ensemble
We investigate the spectral statistics of Hermitian matrices in which the elements are chosen uniformly from U (1), called the uni-modular ensemble (UME), in the limit of large matrix size. Using three complimentary methods; a supersymmetric integration method, a combinatorial graph-theoretical analysis and a Brownian motion approach, we are able …