Prediction of the mean path of random walkers

A random walker is allowed to walk on a surface along two orthogonal directions; the possibility to select either of them is a specific function of the number of steps he has performed. Once he has chosen one of the two axis he is also given a possibility to choose a forward or a backward step; this possibility may also be a specific function of the number of steps. In spite of the wide variety of possibilities that may be assigned we herein describe a theoretical method through which the mean path of a large number of walkers may be found. Several numerical examples for random walkers verify the theoretical results for their mean path.