Claims

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1987_12_01_slade: Slade's 1987 theorem gives, for every sufficiently large dimension, a mean-square displacement asymptotic to Dn for the uniform n-step self-avoiding walk, so d_k(n) << n^{1/2} for all large k; refereed.

1991_10_01_hara_slade: Hara and Slade's theorem gives, for every k at least 5, mean-square displacement Dn(1 + O(n^{-eps})) for the uniform n-step self-avoiding walk on Z^k, so d_k(n) << n^{1/2}; announced 1991, proved in two 1992 papers.

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