2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/57068In [BEI] we introduced a Levy process on a hierarchical lattice which is four dimensional, in the sense that the Green's function for the process equals 1/x^2. If the process is modified so as to be weakly self-repelling, it was shown that at the critical killing rate (mass-squared) β^c, the Green's function behaves like the free one. - Now we analyze the end-to-end distance of the model and show that its expected value grows as a constant times \sqrt{T} log^{1/8}T (1+O((log log T)/log T)), which is the same law as has been conjectured for self-avoiding walks on the simple cubic lattice Z^4. The proof uses inverse Laplace transforms to obtain the end-to-end distance from the Green's function, and requires detailed properties of the Green's function throughout a sector of the complex βplane. These estimates are derived in a companion paper [math-ph/0205028].29 pages, v2: referencesMathematical PhysicsStatistical MechanicsProbability82B41, 82B28, 82B27, 81T60, 81T17, 60K35, 60G18text