A Note on Truncated Long-Range Percolation with Heavy Tails on Oriented Graphs

Autor(es)

Alves, C. ^[1] ; Hilario, M. R. ^[2] ; De Lima, B. N. B. ^[2] ; Valesin, D. ^[3]

Afiliação do(s) autor(es)

^[1] Univ Estadual Campinas, Dept Estat, IMECC, Rua Sergio Buarque de Holanda 651, BR-13083859 Campinas, SP - Brazil

^[2] Univ Fed Minas Gerais, Dept Matemat, Av Antonio Carlos 6627, CP 702, BR-30123970 Belo Horizonte, MG - Brazil

^[3] Univ Groningen, Johann Bernoulli Inst, Nijenborgh 9, NL-9747 AG Groningen - Netherlands

• Tipo de documento: Artigo Científico
• Fonte: Journal of Statistical Physics; v. 169, n. 5, p. 972-980, DEC 2017.
• Citações Web of Science: 0

Resumo

We consider oriented long-range percolation on a graph with vertex set Z(d) x Z(+) and directed edges of the form <(x, t), (x + y, t + 1)>, for x, y in Z(d) and t is an element of Z(+). Any edge of this form is open with probability p(y), independently for all edges. Under the assumption that the values p(y) do not vanish at infinity, we show that there is percolation even if all edges of length more than k are deleted, for k large enough. We also state the analogous result for a long-range contact process on Z(d). (AU)

• Processo FAPESP: 13/24928-2 - Passeios aleatórios e percolação dependente
• Beneficiário: Caio Teodoro de Magalhães Alves
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado