The distribution of the number of points of the closed simple random walk, visited a given number of times (the -multiple point range) is analysed by a graph based approach. A general expression for the moments is derived. In this paper the joint generating function for dimension one is...

The problem of restricted random walks of fixed dimension and finite memory is considered using extension of methods discussed earlier. Inversion of recursion relations, derived in Ref. 1, is derived and recursion relations for restricted random walks of fixed dimension and four and six step...

In this paper, we show that for (i) simple random walks and (ii) random walks with exclusion of immediate reversals it is possible to partition the set of walks into different sub-lattices according to the number of axis directions in which the steps are made. We also show that for (i) and (ii)...

In a landscape composed of randomly distributed sites in Euclidean space, a walker ("tourist") goes to the nearest one that has not been visited in the last steps. This procedure leads to trajectories composed of a transient part and a final cyclic attractor of period The tourist walk presents a...

An efficient stock market plays an important role in stimulating economic development through providing a channel for mobilising domestic savings and facilitating the allocation of financial resources from dormant to more productive activities. This paper evaluates the Ugandan Securities...