Autor(es)

Cerqueira, Andressa ; Garcia, Nancy L.

• Tipo de documento: Artigo Científico
• Fonte: Journal of Mathematical Physics; v. 63, n. 4, p. 21-pg., 2022-04-01.

Resumo

We consider a random graph model on Z(d) that incorporates the interplay between the statistics of the graph and the underlying space where the vertices are located. Based on a graphical construction of the model as the invariant measure of a birth and death process, we prove the existence and uniqueness of a measure defined on graphs with vertices in Z(d), which coincides with the limit along the measures over graphs with the finite vertex set. As a consequence, theoretical properties, such as exponential mixing of the infinite volume measure and central limit theorem for averages of a real-valued function of the graph, are obtained. Moreover, a perfect simulation algorithm based on the clan of ancestors is described in order to sample a finite window of the equilibrium measure defined on Z(d).& nbsp;& nbsp;Published under an exclusive license by AIP Publishing. (AU)

• Processo FAPESP: 13/07699-0 - Centro de Pesquisa, Inovação e Difusão em Neuromatemática - NeuroMat
• Beneficiário: Oswaldo Baffa Filho
• Modalidade de apoio: Auxílio à Pesquisa - Centros de Pesquisa, Inovação e Difusão - CEPIDs
• Processo FAPESP: 17/10555-0 - Modelagem estocástica de sistemas interagentes
• Beneficiário: Fabio Prates Machado
• Modalidade de apoio: Auxílio à Pesquisa - Temático