Rodrigo Silva Gonzalez, Juliana Militao Berbert, Cesar Augusto Sangaletti Tercariol, Wilnice Tavares Reis Oliveira and Alexandre Souto Martinez

A set of N points is randomly spread in a d-dimensional hypercube of unitary edges. The neighborhood statistics among any pair of points is known as the "random point problem" (RPP). A walker can move over these points following the deterministic rule of going, at each time step, to the nearest site not visited in the previous µ steps. This partially self-avoiding walk is known as "deterministic tourist walk" (DTW). Here we present some results on the RPP and on dynamic aspects of the DTW.

Tourist walks, disordered media, partially self-avoiding walks.

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