Abstract
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 . Previous work considered the case of a flight PDF decaying as [Weeks et al., Physica D 97, 291 (1996)]; leftward and rightward flights occurred with differing probabilities and velocities. In addition to these asymmetries, the present strongly asymmetric model uses distinct flight PDFs for leftward and rightward flights: and , with . We calculate the dependence of the variance exponent on the PDF exponents , and . We find that 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 Lévy distribution. When the smallest decay exponent is between 3/2 and 3, the motion is superdiffusive . When the smallest exponent is between 1 and 3/2, the motion can be subdiffusive ; this is in contrast with the case with μ=η.
- Received 21 November 1997
DOI:https://doi.org/10.1103/PhysRevE.57.4915
©1998 American Physical Society