## The Annals of Probability

### Self-Avoiding Walk on a Hierarchical Lattice in Four Dimensions

#### 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

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