Survival Probability for Kinetic Self-Avoiding Walks

The fact that a kinetic self-avoiding walk can only meet topologically connected lines of occupied sites (instead of isolated points) is shown to have important consequences for the asymptotic behavior. The exponent of the kinetic-growth walk (a model for polymer growth) is in fact $\nu =\frac{3}{\mathrm{}(2+d)\mathrm{}}$ instead of the recently proposed value $\nu =\frac{2}{\mathrm{}(d+1\mathrm{})\mathrm{}}$. Especially for $d=3\mathrm{}$, however, the asymptotic behavior is reached only for very long walks ($N\gg {10}^6$). This explains why numerical data seem to indicate lower values for $\nu$.