Brydges, David; Evans, Steven N.; Imbrie, John Z. Self-avoiding walk on a hierarchical lattice in four dimensions. (English) Zbl 0742.60067 Ann. Probab. 20, No. 1, 82-124 (1992). Summary: We define a Lévy 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. Cited in 1 ReviewCited in 22 Documents MSC: 60G50 Sums of independent random variables; random walks Keywords:self-avoiding walk; supersymmetry; Grassman integral; renormalization group; Lévy process; hierarchical lattice PDFBibTeX XMLCite \textit{D. Brydges} et al., Ann. Probab. 20, No. 1, 82--124 (1992; Zbl 0742.60067) Full Text: DOI