Two-Dimensional Random Interlacements and Late Points for Random Walks

Autor(es)

Comets, Francis ^[1] ; Popov, Serguei ^[2] ; Vachkovskaia, Marina ^[2]

Afiliação do(s) autor(es)

^[1] Univ Paris 07, Math, Case 7012, F-75205 Paris 13 - France

^[2] Univ Estadual Campinas, UNICAMP, Dept Stat, Inst Math Stat & Sci Computat, Rua Sergio Buarque de Holanda 651, BR-13083859 Campinas, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: Communications in Mathematical Physics; v. 343, n. 1, p. 129-164, APR 2016.
• Citações Web of Science: 3

Resumo

We define the model of two-dimensional random interlacements using simple random walk trajectories conditioned on never hitting the origin, and then obtain some properties of this model. Also, for a random walk on a large torus conditioned on not hitting the origin up to some time proportional to the mean cover time, we show that the law of the vacant set around the origin is close to that of random interlacements at the corresponding level. Thus, this new model provides a way to understand the structure of the set of late points of the covering process from a microscopic point of view. (AU)

• Processo FAPESP: 14/06815-9 - Passeios aleatórios e outros sistemas aleatórios nos grafos
• Beneficiário: Serguei Popov
• Modalidade de apoio: Bolsas no Exterior - Pesquisa
• Processo FAPESP: 14/06998-6 - Passeios aleatórios e modelos de crescimento
• Beneficiário: Marina Vachkovskaia
• Modalidade de apoio: Bolsas no Exterior - Pesquisa
• Processo FAPESP: 09/52379-8 - Modelagem estocástica de sistemas interagentes
• Beneficiário: Fabio Prates Machado
• Modalidade de apoio: Auxílio à Pesquisa - Temático