  Employing the currently discussed notion of pseudo-Hermiticity, we define a
pseudo-unitary group. Further, we develop a random matrix theory which is
invariant under such a group and call this ensemble of pseudo-Hermitian random
matrices as the pseudo-unitary ensemble. We obtain exact results for the
nearest-neighbour level spacing distribution for (2 X 2) PT-symmetric
Hamiltonian matrices which has a novel form, s log (1/s) near zero spacing.
This shows a level repulsion in marked distinction with an algebraic form in
the Wigner surmise. We believe that this paves way for a description of varied
phenomena in two-dimensional statistical mechanics, quantum chromodynamics, and
so on.
