The Annals of Probability

Self-Avoiding Walk on a Hierarchical Lattice in Four Dimensions

David Brydges, Steven N. Evans, and John Z. Imbrie

Full-text: Open access

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.

Article information

Source
Ann. Probab., Volume 20, Number 1 (1992), 82-124.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176989919

Digital Object Identifier
doi:10.1214/aop/1176989919

Mathematical Reviews number (MathSciNet)
MR1143413

Zentralblatt MATH identifier
0742.60067

JSTOR
links.jstor.org

Subjects
Primary: 60J15
Secondary: 82A25 82A41

Keywords
Self-avoiding walk supersymmetry Grassman integral renormalization group

Citation

Brydges, David; Evans, Steven N.; Imbrie, John Z. Self-Avoiding Walk on a Hierarchical Lattice in Four Dimensions. Ann. Probab. 20 (1992), no. 1, 82--124. doi:10.1214/aop/1176989919. https://projecteuclid.org/euclid.aop/1176989919


Export citation