Self-Avoiding Walk on a Hierarchical Lattice in Four Dimensions
Brydges, David ; Evans, Steven N. ; Imbrie, John Z.
Ann. Probab., Tome 20 (1992) no. 4, p. 82-124 / Harvested from Project Euclid
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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.
Publié le : 1992-01-14
Classification:  Self-avoiding walk,  supersymmetry,  Grassman integral,  renormalization group,  60J15,  82A25,  82A41 
@article{1176989919,
     author = {Brydges, David and Evans, Steven N. and Imbrie, John Z.},
     title = {Self-Avoiding Walk on a Hierarchical Lattice in Four Dimensions},
     journal = {Ann. Probab.},
     volume = {20},
     number = {4},
     year = {1992},
     pages = { 82-124},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176989919}
}

Brydges, David; Evans, Steven N.; Imbrie, John Z. Self-Avoiding Walk on a Hierarchical Lattice in Four Dimensions. Ann. Probab., Tome 20 (1992) no. 4, pp.  82-124. http://gdmltest.u-ga.fr/item/1176989919/