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An ensemble of 2 x 2 pseudo-Hermitian random matrices is constructed thatpossesses real eigenvalues with level-spacing distribution exactly as for theGaussian Unitary Ensemble found by Wigner. By a re-interpretation of Connes'spectral interpretation of the zeros of the Riemann zeta function, we proposeto enlarge the scope of search of the Hamiltonian connected with the celebratedRiemann Hypothesis by suggesting that the Hamiltonian could also bePT-symmetric (or pseudo-Hermitian).

A PSEUDO-UNITARY ENSEMBLE OF RANDOM MATRICES, PT-SYMMETRY AND THE RIEMANN HYPOTHESIS