Abstract: A lattice random walk is a mathematical representation of movement through random steps on a lattice at discrete times. It is commonly referred to as P´olya's walk when the steps occur to either of the nearest-neighbouring sites. Since Smoluchowski's 1906 derivation of the spatio-temporal dependence of the walk occupation probability in an unbounded one-dimensional lattice, discrete random walks and their continuous counterpart, Brownian walks, have developed over the course of a century into a vast and versatile area of knowledge. Lattice ran...
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Topics: 
Statistical physics