Density of states in coupled chains with off-diagonal disorder

We compute the density of states rho(epsilon) in N coupled chains with random hopping. At zero energy, rho(epsilon) shows a singularity that strongly depends on the parity of N. For odd N, rho(epsilon) proportional to 1/\epsilon ln(3)epsilon\, with and without time-reversal symmetry. For even N, rho(epsilon) proportional to \ln epsilon\ in the presence of time-reversal symmetry, while there is a pseudogap, rho(epsilon) proportional to \epsilon ln epsilon\, in the absence of time-reversal symmetry.