Ergodic crossover in partially self-avoiding stochastic walks

Autor(es)

Berbert, Juliana M. ^[1] ; Gonzalez, Rodrigo Silva ^[2] ; Martinez, Alexandre Souto ^[3]

Afiliação do(s) autor(es)

^[1] Univ Estadual Paulista UNESP, IFT, BR-01156970 Sao Paulo - Brazil

^[2] Univ Fed Vicosa, Inst Ciencias Exatas & Tecnol, BR-38810000 Rio Paranaiba, MG - Brazil

^[3] Univ Sao Paulo, FFCLRP, BR-14040901 Ribeirao Preto, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: Physical Review E; v. 88, n. 3 SEP 11 2013.
• Citações Web of Science: 0

Resumo

Consider a one-dimensional environment with N randomly distributed sites. An agent explores this random medium moving deterministically with a spatial memory mu. A crossover from local to global exploration occurs in one dimension at a well-defined memory value mu(1) = log(2) N. In its stochastic version, the dynamics is ruled by the memory and by temperature T, which affects the hopping displacement. This dynamics also shows a crossover in one dimension, obtained computationally, between exploration schemes, characterized yet by the trajectory size (N-p) (aging effect). In this paper we provide an analytical approach considering the modified stochastic version where the parameter T plays the role of a maximum hopping distance. This modification allows us to obtain a general analytical expression for the crossover, as a function of the parameters mu, T, and N-p. Differently from what has been proposed by previous studies, we find that the crossover occurs in any dimension d. These results have been validated by numerical experiments and may be of great value for fixing optimal parameters in search algorithms. (AU)

• Processo FAPESP: 09/11567-6 - Problemas Espaciais em Dinâmica de Populações
• Beneficiário: Juliana Militão da Silva Berbert
• Modalidade de apoio: Bolsas no Brasil - Doutorado