Two-Dimensional Random Interlacements and Late Points for Random Walks

Author(s)

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

Affiliation

^[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

• Document type: Journal article
• Source: Communications in Mathematical Physics; v. 343, n. 1, p. 129-164, APR 2016.
• Web of Science Citations: 3

Abstract

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)

• FAPESP's process: 14/06815-9 - Random walks and other stochastic systems on graphs
• Grantee: Serguei Popov
• Support Opportunities: Scholarships abroad - Research
• FAPESP's process: 14/06998-6 - Random walks and growth models
• Grantee: Marina Vachkovskaia
• Support Opportunities: Scholarships abroad - Research
• FAPESP's process: 09/52379-8 - Stochastic modeling of interacting systems
• Grantee: Fabio Prates Machado
• Support Opportunities: Research Projects - Thematic Grants