Fisher's scaling and dualities at thigh energy in E(∞) spaces

The note outlines an extension of the well-known Fisher scaling relationship gamma = nu (2 - eta) using duality to transform the Ambjorn-Castro and Parisi's result for the Hausdorff dimension d(H) = 1/nu = 4 of a branched random walk to that of the polymerized E(infinity) space namely [dim(H) b(infinity)] = 4 + phi (3) = 4236067. Relation to the Josephson nud = 2 - alpha and related scaling are also discussed: (C) 2001 Elsevier Science Ltd. All rights reserved.