Multifractality in random networks with power-law decaying bond strengths

Autor(es)

Vega-Oliveros, Didier A. ; Mendez-Bermulez, J. A. ; Rodrigues, Francisco A.

• Tipo de documento: Artigo Científico
• Fonte: PHYSICAL REVIEW E; v. 99, n. 4, p. 7-pg., 2019-04-10.

Resumo

In this paper we demonstrate numerically that random networks whose adjacency matrices A are represented by a diluted version of the power-law banded random matrix (PBRM) model have multifractal eigenfunctions. The PBRM model describes one-dimensional samples with random long-range bonds. The bond strengths of the model, which decay as a power-law, are tuned by the parameter mu as A(mm) proportional to vertical bar m - nVERBAR;(-mu ); while the sparsity is driven by the average network connectivity alpha: for alpha = 0 the vertices in the network are isolated and for alpha = 1 the network is fully connected and the PBRM model is recovered. Though it is known that the PBRM model has multifractal eigenfunctions at the critical value mu = mu(c) = 1, we clearly show [from the scaling of the relative fluctuation of the participation number I-2 as well as the scaling of the probability distribution functions P(ln I-2)] the existence of the critical value mu(c) (math) mu(c) (alpha) for alpha < 1. Moreover, we characterize the multifractality of the eigenfunctions of our random network model by the use of the corresponding multifractal dimensions D-q, that we compute from the finite network-size scaling of the typical eigenfunction participation numbers exp < ln I-q >. (AU)

• Processo FAPESP: 13/07375-0 - CeMEAI - Centro de Ciências Matemáticas Aplicadas à Indústria
• Beneficiário: Francisco Louzada Neto
• Modalidade de apoio: Auxílio à Pesquisa - Centros de Pesquisa, Inovação e Difusão - CEPIDs
• Processo FAPESP: 16/23698-1 - Processos Dinâmicos em Aprendizado de Máquina baseados em Redes Complexas
• Beneficiário: Didier Augusto Vega Oliveros
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado
• Processo FAPESP: 13/26416-9 - Modelagem de processos dinâmicos em redes complexas
• Beneficiário: Francisco Aparecido Rodrigues
• Modalidade de apoio: Auxílio à Pesquisa - Regular