title: Deterministic walks in random media.
abstract: Deterministic walks over a random set of N points in one and two dimensions ( d = 1,2) are considered. Points ("cities") are randomly scattered in R(d) following a uniform distribution. A walker ("tourist"), at each time step, goes to the nearest neighbor city that has not been visited in the past tau steps. Each initial city leads to a different trajectory composed of a transient part and a final p-cycle attractor. Transient times (for d = 1,2) follow an exponential law with a tau-dependent decay time but the density of p cycles can be approximately described by D(p)proportional to p(-alpha(tau)). For tau>>1 and tau/N<<1, the exponent is independent of tau. Some analytical results are given for the d = 1 case.
authors.affiliation: Faculdade de Filosofia, Ciências e Letras de Ribeirão Preto, Universidade de São Paulo, Avenida Bandeirantes 3900, CEP 14040-901, Ribeirão Preto, SP, Brazil.
authors.forename: G F
authors.initials: GF
authors.lastname: Lima
authors.forename: A S
authors.initials: AS
authors.lastname: Martinez
authors.forename: O
authors.initials: O
authors.lastname: Kinouchi