Open Access
January, 1992 Self-Avoiding Walk on a Hierarchical Lattice in Four Dimensions
David Brydges, Steven N. Evans, John Z. Imbrie
Ann. Probab. 20(1): 82-124 (January, 1992). DOI: 10.1214/aop/1176989919


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.


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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.


Published: January, 1992
First available in Project Euclid: 19 April 2007

zbMATH: 0742.60067
MathSciNet: MR1143413
Digital Object Identifier: 10.1214/aop/1176989919

Primary: 60J15
Secondary: 82A25 , 82A41

Keywords: Grassman integral , renormalization group , Self-avoiding walk , supersymmetry

Rights: Copyright © 1992 Institute of Mathematical Statistics

Vol.20 • No. 1 • January, 1992
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