Conductance distribution at the mobility edge

It is shown that, for a system at the mobility edge, the conductance distribution ${\mathit{P}}_{\mathit{L}}$(g) approaches an entirely universal function ${\mathit{P}}^{\mathrm{*}}$(g) when the size L of the system increases. The function ${\mathit{P}}^{\mathrm{*}}$(g) depends on dimensionality d alone and does not depend on any details of the model. In obtaining ${\mathit{P}}^{\mathrm{*}}$(g) use was made of the conductance cumulants calculated by Altshuler, Kravtosv, and Lerner [Phys. Lett. A 134, 488 (1989)]. The calculations are limited to spatial dimension d=2+ε, where ε is a small number.