Abstract
Using an expansion based on the renormalization group philosophy we prove that for aT step weakly self-avoiding random walk in five or more dimensions the variance of the endpoint is of orderT and the scaling limit is gaussian, asT→∞.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Domb, C.: Self-avoiding random walk on lattices. In: Stochastic processes in chemical physics. Shuler, K. E. (ed.), pp. 229–260. New York: Wiley 1969
Aizenman, M.: Geometric analysis of φ4 fields and Ising models. Parts I and II. Commun. Math. Phys.86, 1–48 (1982)
Fröhlich, J.: On the triviality of λφ 4 d theories and the approach to the critical point ind≧4 dimensions. Nucl. Phys. B200, 281–296 (1982)
Lawler, G.: A self-avoiding random walk. Duke Math. J.47, 655–693 (1980)
Fröhlich, J. (ed.): Scaling and self-similarity in physics — Renormalization in statistical mechanics and dynamics. Boston, Basel, Stuttgart: Birkhäuser 1983
Fröhlich, J.: Cargèse lectures
Author information
Authors and Affiliations
Additional information
Communicated by A. Jaffe
Dedicated to the memory of Kurt Symanzik whose profound contributions have guided and inspired us
Work partially supported by N.S.F. Grant DMR 81-00417
A. P. Sloan Foundation Fellow. Work partially supported by N.S.F. Grant MCS 82-02115
Rights and permissions
About this article
Cite this article
Brydges, D., Spencer, T. Self-avoiding walk in 5 or more dimensions. Commun.Math. Phys. 97, 125–148 (1985). https://doi.org/10.1007/BF01206182
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01206182