Random surface semiregular triangulated coverings

A procedure for triangulation of random surfaces is proposed in order to overcome the severe difficulties posed by the theorem of Ambjørn, Durhuus and Fröhlich. Without having to abandon the primitive definition of the action as being equal to the surface area, finite expressions for all the momenta are derived, which lead (in particular) to a consistent definition of the Hausdorff dimension of the surface.