Convergence of self-avoiding random walk to Brownian motion in high dimensions

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, , Citation G Slade 1988 J. Phys. A: Math. Gen. 21 L417 DOI 10.1088/0305-4470/21/7/010

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1 Dept. of Math. & Stat., McMaster Univ., Hamilton, Ont., Canada

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0305-4470/21/7/L417

Abstract

It is proved that, in sufficiently high dimensions, the scaled self-avoiding random walk on the hypercubic lattice converges in distribution to Brownian motion. Convergence of the finite-dimensional distributions was shown elsewhere. In this paper tightness is shown.

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