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Self-avoiding walk on a hierarchical lattice in four dimensions. (English) Zbl 0742.60067

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.

MSC:

60G50 Sums of independent random variables; random walks
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