Density of states in coupled chains with off-diagonal disorder

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