Fisherʹs scaling and dualities at high energy in spaces

The note outlines an extension of the well-known Fisher scaling relationship γ=ν(2−η) using duality to transform the Ambjørn–Castro and Parisiʹs result for the Hausdorff dimension dH=1/ν=4 of a branched random walk to that of the polymerized space namely . Relation to the Josephson νd=2−α and related scaling are also discussed.