Abstract
We define a Levy process on a $d$-dimensional hierarchical lattice. By construction the Green's function for this process decays as $|x|^{2-d}$. For $d = 4$, we prove that the introduction of a sufficiently weak self-avoidance interaction does not change this decay provided the mass $\equiv$ "killing" rate is chosen in a special way, so that the process is critical.
Citation
David Brydges. Steven N. Evans. John Z. Imbrie. "Self-Avoiding Walk on a Hierarchical Lattice in Four Dimensions." Ann. Probab. 20 (1) 82 - 124, January, 1992. https://doi.org/10.1214/aop/1176989919
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