The main part of this thesis is on how the non-Hermiticty of the diffusion-advection model effects its long-time diffusive transport behaviour in the critical dimension d=2. Original calaulations did not properly take into account the non-Hermiticity. We build an approach that takes into account non-hermiticity and allows for a consistent sum of logarithmic corrections. We use an extended space, like in [Chalker-Wang], which (after the rotation exp (i π σ2/4)) is formally equivalent to Nambu-Gorkov space. We found that the transport behaviour was not corrected and that the boundary to the density of complex eigenvalues collapsed to the real line as \omega tends to zero. We also investigated mesoscopic fluctuations in density distribution and found it to have log-normal tails.