- PDF copy
We present a model of one-dimensional asymmetric random walks. Random walkers alternate between flights (steps of constant velocity) and sticking (pauses). The sticking time probability distribution function (PDF) decays as

*P(t) ~ t^{-u}*. Previous work considered the case of a flight PDF decaying as*P(t) ~ t^{-v}*[Weeks et al., Physica D**97**, 291 (1996)]; leftward and rightward flights occurred with differing probabilities and velocities. In addition to these asymmertries, the present strongly asymmetric model uses distinct flight PDFs for leftward and rightward flights:*P_L(t) ~ t^{-v}*and*P_R(t) ~ t^{-w}*, with*v*not equal to*w*. We calculate the dependence of the variance exponent*z*(*sigma^2 ~ t^z*) on the PDF exponents*u*,*v*, and*w*. We find that*z*is determined by the two smaller of the three PDF exponents, and in some cases by only the smallest. A PDF with decay exponent less than 3 has a divergent second moment, and thus is a Levy distribution. When the smallest decay exponent is between 3/2 and 3, the motion is superdiffusive (*1<z<2*). When the smallest exponent is between 1 and 3/2, the motion can be subdiffusive (*z<1*); this is in contrast with the previous results.