Duke Mathematical Journal

A self-avoiding random walk

Gregory F. Lawler

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Article information

Duke Math. J., Volume 47, Number 3 (1980), 655-693.

First available in Project Euclid: 20 February 2004

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60J15
Secondary: 60F17: Functional limit theorems; invariance principles 82A42


Lawler, Gregory F. A self-avoiding random walk. Duke Math. J. 47 (1980), no. 3, 655--693. doi:10.1215/S0012-7094-80-04741-9. https://projecteuclid.org/euclid.dmj/1077314188

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  • [1] Robert M. Anderson, A non-standard representation for Brownian motion and Itô integration, Israel J. Math. 25 (1976), no. 1-2, 15–46.
  • [2] Patrick Billingsley, Convergence of probability measures, John Wiley & Sons Inc., New York, 1968.
  • [3] C. Domb, Self-avoiding random walk on lattices, Stochastic Processes in Chemical Physics ed. K. E. Shuler, John Wiley and Sons, 1969, pp. 229–260.
  • [4] A. Dvoretzky, P. Erdös, and S. Kakutani, Double points of paths of Brownian motion in $n$-space, Acta Sci. Math. Szeged 12 (1950), no. Leopoldo Fejer et Frederico Riesz LXX annos natis dedicatus, Pars B, 75–81.
  • [5] P. Erdős and S. J. Taylor, Some intersection properties of random walk paths, Acta Math. Acad. Sci. Hungar. 11 (1960), 231–248.
  • [6] William Feller, An introduction to probability theory and its applications. Vol. I, Third edition, John Wiley & Sons Inc., New York, 1968.
  • [7] Kiyosi Itô and H. P. McKean, Jr., Potentials and the random walk, Illinois J. Math. 4 (1960), 119–132.
  • [8] Harry Kesten, On the number of self-avoiding walks, J. Mathematical Phys. 4 (1963), 960–969.
  • [9] Simon Kochen and Charles Stone, A note on the Borel-Cantelli lemma, Illinois J. Math. 8 (1964), 248–251.
  • [10] Edward Nelson, Internal set theory: a new approach to nonstandard analysis, Bull. Amer. Math. Soc. 83 (1977), no. 6, 1165–1198.
  • [11] Frank Spitzer, Principles of random walks, Springer-Verlag, New York, 1976.
  • [12] J. M. Hammersley and K. W. Morton, Poor man's Monte Carlo, J. Roy. Statist. Soc. Ser. B. 16 (1954), 23–38; discussion 61–75.