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A Lower Bound for the End-to-End Distance of Self-Avoiding Walk For an $N$-step self-avoiding walk on the hypercubic lattice ${\bf Z}^d$,
we prove that the mean-square end-to-end distance is at least
$N^{4/(3d)}$ times a constant.
This implies that the associated critical exponent $\nu$ is
at least $2/(3d)$, assuming that $\nu$ exists.
Keywords:self-avoiding walk, critical exponent Categories:82B41, 60D05, 60K35 |