ANOMALOUS DIFFUSION RESULTING FROM STRONGLY ASYMMETRIC RANDOM-WALKS

We present a model of one-dimensional asymmetric random walks. Random walkers alternate between flights (steps of constant velocity) and sti cking (pauses). The sticking time probability distribution function (P DF) decays as P(t)similar to t(-nu). Previous work considered the case of a flight PDF decaying as P(t)similar to t(-mu) [Weeks ct al., Phys ica D 97, 291 (1996)]; leftward and rightward flights occurred with di ffering probabilities and velocities. In addition to these asymmetries , the present strongly asymmetric model uses distinct flight PDFs for leftward and rightward flights: P-L(t)similar to t(-mu) and P-R(t)simi lar to t(-eta) With mu not equal eta . We calculate the dependence of the variance exponent gamma (sigma(2) similar to t(gamma)) On the PDF exponents nu, mu, and eta. We find that gamma is determined by the two smaller of the three PDF exponents, and in some cases by only the sma llest. A PDF with decay exponent less than 3 has a divergent second mo ment, and thus is a Levy distribution. When the smallest decay exponen t is between 3/2 and 3, the motion is superdiffusive (1 < y < 2). When the smallest exponent is between 1 and 3/2, the motion can be subdiff usive (y < 1); this is in contrast with the case with mu=eta.