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(Referência obtida automaticamente do Web of Science, por meio da informação sobre o financiamento pela FAPESP e o número do processo correspondente, incluída na publicação pelos autores.)

Exact solution of an anisotropic 2D random walk model with strong memory correlations

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Autor(es):
Cressoni, J. C. [1, 2] ; Viswanathan, G. M. [3] ; da Silva, M. A. A. [1]
Número total de Autores: 3
Afiliação do(s) autor(es):
[1] Univ Sao Paulo, Dept Fis & Quim, FCFRP, BR-14040903 Ribeirao Preto, SP - Brazil
[2] Univ Fed Alagoas, Inst Fis, BR-57072970 Maceio, AL - Brazil
[3] Univ Fed Rio Grande do Norte, Dept Fis Teor & Expt, BR-59078900 Natal, RN - Brazil
Número total de Afiliações: 3
Tipo de documento: Artigo Científico
Fonte: Journal of Physics A-Mathematical and Theoretical; v. 46, n. 50 DEC 20 2013.
Citações Web of Science: 9
Resumo

Over the last decade, there has been progress in understanding one-dimensional non-Markovian processes via analytic, sometimes exact, solutions. The extension of these ideas and methods to two and higher dimensions is challenging. We report the first exactly solvable two-dimensional (2D) non-Markovian random walk model belonging to the family of the elephant random walk model. In contrast to Levy walks or fractional Brownian motion, such models incorporate memory effects by keeping an explicit history of the random walk trajectory. We study a memory driven 2D random walk with correlated memory and stops, i.e. pauses in motion. The model has an inherent anisotropy with consequences for its diffusive properties, thereby mixing the dominant regime along one dimension with a subdiffusive walk along a perpendicular dimension. The anomalous diffusion regimes are fully characterized by an exact determination of the Hurst exponent. We discuss the remarkably rich phase diagram, as well as several possible combinations of the independent walks in both directions. The relationship between the exponents of the first and second moments is also unveiled. (AU)

Processo FAPESP: 11/13685-6 - Modelagem analítica e computacional de sistemas difusivos
Beneficiário:Marco Antonio Alves da Silva
Linha de fomento: Auxílio à Pesquisa - Pesquisador Visitante - Brasil
Processo FAPESP: 11/06757-0 - Processos difusivos: caminhantes aleatórios com memória
Beneficiário:Marco Antonio Alves da Silva
Linha de fomento: Auxílio à Pesquisa - Regular