Gruppo di Fisica Statistica

The self-directed walk is studied in one dimension. In this walk with memory the jump probability is given by WN+or-(i)=(1+exp(+or-g Delta N(i)))-1 where Delta N is the difference between the number of times the sites in the forward and backward directions have been visited after N steps. When g>O there is a crossover between a Gaussian random walk and an intermediate regime where the radius of gyration grows like N2 followed by a crossover to the asymptotic regime where the walk is directed. When g<0 a single crossover is obtained between the Gaussian random walk and a saturation regime at large N when the walk is self-attracting.