Exploratory behavior, trap models, and glass transitions.
A random walk is performed on a disordered landscape composed of N sites randomly and uniformly distributed inside a d-dimensional hypercube. The walker hops from one site to another with probability proportional to exp[-betaE(D)], where beta=1/T is the inverse of a formal temperature and E(D) is an arbitrary cost function which depends on the hop distance D. Analytic results indicate that, if E(D)=D(d) and N--> infinity, there exists a glass transition at beta(d)=pi(d/2)/[(d/2)Gamma(d/2)]. Below T(d), the average trapping time diverges and the system falls into an out-of-equilibrium regime with aging phenomena. A Lévy flight scenario and applications of exploratory behavior are considered.
Martinez
Alexandre S
AS
Faculdade de Filosofia, Ciências e Letras de Ribeirão Preto, Universidade de São Paulo, Avenida Bandeirantes 3900, 14040-901 Ribeirão Preto, São Paulo, Brazil. martinez@dfm.ffclrp.usp.br
Kinouchi
Osame
O
Risau-Gusman
Sebastian
S