  We calculate, using numerical methods, the Lyapounov exponent gamma(E) and
the density of states rho(E) at energy E of a one-dimensional non-Hermitian
Schroedinger equation with off-diagonal disorder. For the particular case we
consider, both gamma(E) and rho(E) depend only on the modulus of E. We find a
pronounced maximum of rho(|E|) at energy E=2/sqrt(3), which seems to be linked
to the fixed point structure of an associated random map. We show how the
density of states rho(E) can be expanded in powers of E. We find rho(|E|) =
1/pi^2 + 4/(3 pi^3) |E|^2 + ... This expansion, which seems to be asymptotic,
can be carried out to an arbitrarily high order.

Statistical Mechanics